Pep Guardiola has warned that Manchester City are growing in resilience after Erling Haaland and Phil Foden secured the side’s fifth win in succession and maintained pressure on the Premier League leaders Arsenal.

City gained revenge for their FA Cup final defeat by Crystal Palace in May with a ruthless 3-0 win at Selhurst Park after they saw off Real Madrid in the Champions League in midweek. It means they have won all five matches since enduring successive defeats against Newcastle and Bayer Leverkusen at the end of November and are back to within two points of Arsenal.

Guardiola believes that his team have shown real signs of improvement over the past few weeks and he pointed to previous sides that had to learn to win the hard way.

“From experience when you win in the past you believe the past is always perfect – brilliant, red carpets,” he said. “When we won 100 points and all the titles we had a lot of games like today and the resilience was part of that. Every plan from every manager wants to do the best but there are moments where you struggle.

“Madrid was not a perfect game but it is a step that we were there and we fought, whatever happens we fought unbelievably to achieve that. That builds something for that and after we will see. We are in a better position than last season, we are close and this is what we are here to do.”

City came under huge pressure against Palace in the first half but took the lead through Haaland’s header before Foden doubled their advantage. A late Halaand penalty – his 17th Premier League goal of the season – continued Guardiola’s record of never having lost at Selhurst Park, but the City manager paid tribute to the performance of his defence and in particular Rúben Dias.

“They played together a lot lately for obvious reasons and when you are playing together the connection between the back four is so important,” he said. “The pace and composure for both full-backs, the leadership from Rúben. Rúben is an incredible leader, his professionalism, the day before, the day after, how he leads his teammates vocally. He’s an incredible signing for many years to come, he’s a real leader.”

Oliver Glasner said his side must learn to be more ruthless against the top teams. “The result doesn’t reflect the performance,” the Palace manager said. “We have to accept it. City were better in the boxes and more efficient than we were.”