David Moyes refused to criticise the players who missed all Everton’s penalties in a 3-0 shootout defeat to Sunderland in the club’s first FA Cup tie at Hill Dickinson Stadium.

Unconvincing efforts from James Garner, who had scored from the spot in the 89th minute to cancel out Enzo Le Fée’s first-half strike, Thierno Barry and Beto were all saved by Robin Roefs. It was the first time in Everton’s history they had failed to score a single penalty in a shootout, and they became only the second top-flight team to lose an FA Cup shootout without scoring after Blackburn, also against Sunderland, in 2003.

“I don’t think you blame anybody when you lose a penalty shootout. It’s something that can happen, the goalkeeper is there to make saves,” said Moyes. “But I think there is a way to lose if you’re going to do that. It felt as if we didn’t do it in that way and that’s why we have all walked away with huge disappointment.”

Lamine Cissé scored a stunning 88th-minute winner as 2011 FA Cup runners-up Stoke beat Championship leaders Coventry 1-0 at the bet365 Stadium. The home side wasted good chances in the opening half and 1987 winners Coventry hit the woodwork twice in the second. But with the tie heading for extra time, Cissé scored a spectacular long-range effort – his first goal for the club – to extend Coventry’s winless run to four matches.

Frank Lampard, who made eight changes, said he was giving priority to their league campaign. “Of course, we wanted to win the game. The FA Cup is a beautiful, beautiful thing. I know it, I have won it. But the reality for teams fighting at the top of the Championship, it is very clear what we want and what we need to do.”

Rob Edwards said his Wolves side are slowly improving after they cruised to a 6-1 victory over Shrewsbury, which included Jorgen Strand Larsen’s first hat-trick for the club. The forward has been linked with a move away from Molineux, and Edwards refused to rule out an exit in the January. “He’s working hard, his attitude has been great and he understood why he hasn’t started the last few games. His commitment has never wavered. He was brilliant today in everything he did.”

Harry Wilson, Emile Smith Rowe and Kevin all scored in the second half as Fulham fought from behind to secure a 3-1 victory against Middlesbrough. Hayden Hackney gave the second-placed Championship side a deserved lead in the opening period at Craven Cottage before substitute Wilson struck a brilliant equaliser on the hour mark. Tommy Conway hit the crossbar for Middlesbrough moments later only to see Smith Rowe put Fulham ahead with 13 minutes to go. Kevin put the gloss on the victory with a third for the hosts in stoppage time.

Marco Silva admitted he remains uncertain about Wilson’s future, with the 28-year-old out of contract at the end of the season. “I don’t know if I am going to have him in one week, 15 days, three months or at the end of the season, with good or bad news. I cannot guarantee anything. What I do know, is that he is playing the best football of his career. He is in the best moment of his career.”

Leicester avoided a potential shock by winning 2-0 at Cheltenham, with Patson Daka opening the scoring, and Stephy Mavididi scoring on half-time to put the tie beyond the reach of the team 18th in League Two. Martí Cifuentes, who made eight changes, praised his side’s “energy and desire”, adding: “The FA Cup is a beautiful competition and we want to go as far as possible. You see every year there is a surprise and Crystal Palace lost, so we didn’t want to be that surprise.”

Ashley Barnes struck twice as Burnley put their Premier League worries on hold to ease into the fourth round with a 5-1 win over Millwall. The 36-year-old scored his first goal of the season early on and added his second midway through the second half. Loum Tchaouna, Jaidon Anthony and substitute Jaydon Banel also found the net, while Millwall hit an added-time consolation through Josh Coburn.

Southampton survived a scare on their way to ending a six-game winless run with a hard-fought 3-2 victory at equally out-of-form Doncaster. The sides’ first ever meeting in this competition offered Tonda Eckert’s stumbling Southampton the ideal chance to get back to winning ways after their recent Championship problems.

The away side seemed set to cruise through after Cameron Bragg, Cameron Archer and Kuryu Matsuki scored first-half goals against the side 23rd in League One, only for Doncaster to expose familiar frailties. Grant McCann’s men, who also came into this without a win in six games, pulled back two goals through Matty Pearson and Jordan Gibson as visitors wobbled early in the second half. However, debutant Daniel Peretz’s double save in stoppage time helped Southampton avoid embarrassment.

Jaden Philogene and Jacob Greaves scored as Ipswich beat Blackpool 2-1. A trademark curling finish from Philogene and header from Greaves had the Championship side clear, before Ashley Fletcher pulled a goal back for the League One visitors with an added-time penalty.

Brentford cruised into the fourth round, easing past Sheffield Wednesday 2-0. Goals from Keane Lewis-Potter and Mathias Jensen earned them victory at Hillsborough. The scoreline did not reflect Brentford’s total domination and it would have been far more handsome but for a heroic performance from young goalkeeper Pierce Charles. Only an injury to England international Jordan Henderson soured Brentford’s afternoon.

Birmingham fought off a late Cambridge fightback to win 3-2. Despite there being 40 places between the sides, League Two Cambridge might have fancied their chances beforehand after suffering only one home defeat this season. But they were two down at the break thanks to Kai Wagner’s deflected effort, his first goal since signing from Philadelphia Union, and Kyogo Furuhashi’s clinical finish.

The third goal came 11 minutes from the end as the hosts gave possession away and Tommy Doyle fed Marvin Ducksch, who rolled the ball into the far corner. Cambridge responded immediately as Louis Appéré’s determined play helped work the ball to substitute Sullay Kaikai, who also found the far corner with a precise finish. Kaikai scored a second a minute from time with an excellent thumping strike, but Birmingham saw out stoppage time to progress to round four.

Emil Riis hit a hat-trick as Bristol City delivered a thumping 5-1 victory over Championship rivals Watford at Ashton Gate. Riis struck an early opener, created the second for Anis Mehmeti and then claimed two more in nine second-half minutes as the City scored five goals for the second successive home game.

National League Boreham Wood’s adventure was ended by Burton, with strikes from Kyran Lofthouse, Fábio Tavares, Dylan Williams and JJ McKiernan adding to a Charlie O’Connell own goal in a thumping 5-0 victory for the League One side.