An ominous defeat drove Roberto Martínez to try to show that he can, in fact, build a strong defence. Pointing to the positives amid amid this 2-1 loss against Manchester Unitedand the strides he believes Everton have made during his three‑year tenure, the Spaniard trumpeted his defiance of the fans who want him sacked and declared that he deserves to be allowed to “drive the club forward” by making “big moves” this summer, thanks to the club’s new financial backing.

This semi-final elimination, following an exit at the same stage of the Capital One Cup, leaves Everton with little to play for this season other than avoiding a second successive finish in the bottom half of the Premier League. That is a situation many of their fans deem unacceptable for a squad that the manager has described as the club’s best in a generation. Farhad Moshiri, the Iranian billionaire who bought a 49.9% stake in Everton last month, also has higher targets than that but Martínez, who talks to Moshiri regularly, claims he has shown he can meet the club’s ambitions.

“I just want to believe, with the work I have done for the last three years, there are signs there that we are getting close to challenging for silverware and where Everton should be,” he said. “We developed young players, gave them big roles and they reacted, and showed character, flair and drive in the biggest football arena.

“In the first season we had a [club] record number of points in the Premier League and in the second the experience of Europe. We gave young players big roles and have not invested money but managed assets. We were very unfairly stopped from being in the League Cup final and that never stopped us wanting to come to Wembley. There are signs in the three years I could have earned the opportunity to drive the club forward and I am sure we can fulfil our expectations. I am very much attached to it.”

Martínez said that with the backing of Moshiri he will be able to take the club to heights not reached for years. “The introduction of the new shareholder brings a different approach to the new squad. We have the finances to compete with anyone within the fair play rules. That can only be a help. I see it no other way.

“The difficulty is building a squad without the money other teams have while they are fighting for the same aims you have. The arrival of the new shareholder is terrific, positive news for the future and helps you build squads.

“Clearly, at the end of the season we will need to make big moves and make sure we start the season with a strong team that is ready to fight and play the way we have to play. [Moshiri’s] vision is to become a winning team and bring Everton to where we all want it. That goes into the footballing style. It is a shared vision.” Asked how certain he was that he would still be Everton’s manager come the summer, Martínez replied: “You’re asking the wrong man.”

The Spaniard said he took heart from the experiences of Everton’s two-time title-winning manager, the late Howard Kendall, and also from the team’s second-half improvement at Wembley, which might not have been fruitless if Romelu Lukaku had not had a penalty saved by David de Gea before Chris Smalling equalised with an own goal and Anthony Martial inflicted a killer blow in stoppage time.

“I draw inspiration from big, big figures from our football club – and no one more than Howard Kendall, who always said as a football club we react in the best possible way,” Martínez said, determined to remain positive. “Facing adversity [against United] our second‑half performance is exactly that. It was as dominant as you could see in a semi-final against a team like Manchester United.

“Without being at our best we could not get into the rhythm in the first half and we showed incredible maturity and mental strength to dig in. The second half is us – confidence, belief and fast football with attacking threat. We missed a penalty and it never affected us. Conceding in injury time is a major blow that we did not deserve. I was pleased the players represented our football club in a way we know they can in the second half. They enjoyed their football.”

United enjoyed it more. There were certainly encouraging signs for Louis van Gaal’s side, especially the nifty derring-do of young attackers such as Martial and Marcus Rashford, but the older heads know it is too soon for bold declarations. “I don’t want to get carried away,” Michael Carrick said. “Two weeks ago everything was a disaster [after the 3-0 loss at Tottenham] and this doesn’t change the whole thing. We know where we’re at as a team and a club. We know we need to improve, of course we do. We need to be right at the top of the league again. That’s not going to change over the next few weeks. Time will tell how it goes but we need a strong finish in the league and then to come back to Wembley and do it all again.”

Winning the final would be a major boost to this mainly young squad. “You can’t explain what winning a trophy brings,” Carrick said – before proceeding to do exactly that. “It brings belief, confidence. We have got a good team spirit.

“Yes, we’ve had ups and downs along the last two or three years, and things haven’t quite worked how we wanted it to, but you’ve got to keep believing and keep trying to improve, and to win a trophy would give everyone a lift. Hopefully it could be a kick-start.”

Man of the match Anthony Martial (Manchester United)