It was a strange sight to watch one West Ham United fan climb a fence in an attempt to get back into the London Stadium.

After leaving when his team were 2-0 down against Leeds United, he was far from the only person feeling a sense of regret when West Ham scored in the 93rd and 97th minutes to force extra time in their FA Cup quarter-final.

The fan pleaded to be allowed back in but the security guards in their hi-vis jackets showed similar fighting spirit to West Ham’s players on the pitch after Dominic Calvert-Lewin scored a penalty for Leeds in the 75th minute. Hopes of a first Wembley appearance since 2012 (the Championship play-off final) seemed dashed.

There were several empty seats as the match approached stoppage time. After all, many had seen a performance that lacked attacking edge and creative spark — but that changed when Mateus Fernandes’ goal in the 93rd minute brought hope. Those who had not quite reached the exits returned to their seats in the hope of witnessing a dramatic late equaliser.

Axel Disasi, the Chelsea loanee, was the unlikeliest of scorers as he converted Adama Traore’s cross to make it 2-2, with jubilation gripping the stadium, to send the tie into extra time.

Axel Disasi celebrates in front of the West Ham supporters (Mike Hewitt/Getty Images)

But elation was replaced with dejection when West Ham lost 4-2 on penalties, with Jarrod Bowen and Pablo’s spot kicks saved by Lucas Perri, the Leeds goalkeeper. Those who remained applauded the players as they walked to all four corners of the ground. Despite the disappointment, head coach Nuno Espirito Santo insisted he would take the positives as West Ham fight to stay in the Premier League.

“What I saw on the pitch was more important than anything,” Nuno said in his post-match press conference. “What I saw was a group of players that didn’t give up. This is the major lesson that we have to take from today. We cannot allow ourselves for one minute to give up what we have in our hands, the mission that we have to do.

“We require belief, character, handling the pressure — and this is what I saw today. We cannot allow ourselves to spend too much time in sorrow and sadness. I really believe that what we have ahead of us is much, much, much important.”

West Ham dared to dream and their performance in the last 30 minutes bodes well for their top-flight survival hopes. The club are 18th, a point and a place below London rivals Tottenham Hotspur, and their remaining fixtures are against Wolverhampton Wanderers (h), Crystal Palace (a), Everton (h), Brentford (a), Arsenal (h), Newcastle United (a) and Leeds (h).

Their inspired comeback on Sunday to keep the game alive was impressive considering they were without Jean-Clair Todibo and Crysencio Summerville, both sidelined with calf injuries. Before the game, Nuno said the two key players will continue to be assessed but their returns could not come sooner. The head coach made five changes to his starting XI from the 2-0 loss at Aston Villa before the international break, with Alphonse Areola, Kyle Walker-Peters, Maximilian Kilman, Soungoutou Magassa and Traore coming into the side.

Kilman had not played since the fourth-round win against Burton Albion in February but he struggled again, conceding a penalty for a foul on Brenden Aaronson. Kilman was fortunate not to give away a penalty in the first half when he attempted to block on Anton Stach’s shot. Worst of all, Kilman was booed by sections of the fanbase whenever he was in possession. Seldom have many felt the need to turn on their own in such fashion.

Maximilian Kilman concedes the penalty for a foul against Brenden Aaronson (Mike Hewitt/Getty Images)

Areola and Walker-Peters had solid performances, but Magassa failed to impress, lacked defensive awareness for Leeds’ opener via Ao Tanaka and was substituted at half-time. Traore seized his rare start and was applauded when he was substituted in extra time for Ezra Mayers. The winger, who joined from Fulham in January, had his best performance under Nuno and was a bright attacking outlet in Summerville’s absence.

“I’m sad because of how we lost but we have to take the positives,” Traore told The Athletic after the defeat. “We showed great fighting spirit and fought until the end. We lost on penalties but we will try to improve in our next game. We need to move on. We can stay up and the feeling would’ve been better if it were a win but there were positives. I love the identity of the club and the fans who are passionate like me. I want to play and do well under a manager I know.”

Before the start of extra time, actor and fan Danny Dyer danced to the chant about Jarrod Bowen, who is Dyer’s son-in-law. Nuno had inspired words for his players during the team huddle, Summerville tried to gee up Traore, while first-team coach Paco Jemez pulled forward Pablo to one side and gestured the kind of offensive runs he needs to make.

Everyone was aware of what was at stake and euphoria ended prematurely when Taty Castellanos’ goal in the 93rd minute was ruled out for offside. The momentum was still with West Ham and nine minutes later, Pablo’s follow-up strike from Bowen’s shot was also disallowed for offside.

Areola sustained a knock in the dying stages of extra time. Academy prospect Finlay Herrick, 20, was handed his first-team debut and instantly made an impact when he saved Joel Piroe’s penalty in the shootout. Moments beforehand, the goalkeeper watched video clips in the tunnel with goalkeeping coaches Rui Barbosa and Billy Lepine.

But the opportunity to take the lead was squandered when Bowen missed his penalty. Only Walker-Peters and Tomas Soucek converted for West Ham.

“I’m gutted,” Bowen told the club’s official website. “I’ve let people down. It really hurts because we’d done so much to get back in the game. Fin has a brilliant moment saving the first penalty, and when you’re up next, you’re confident of scoring. Sometimes you have these low moments and that’s how it is.”

Now there must be a unified togetherness against Wolves.