Jose Mourinho’s side progressed to the fifth round of the FA Cup with a 3-2 victory over Southampton on Wednesday.
Spurs were outplayed for much of the clash in north London, but Alli believes his side deserve a bit of luck having fallen short of silverware in recent season.s
“It says a lot about the character we have,” he told BT Sport. “To go from such a big game at the weekend [a 2-0 defeat of Manchester City], it’s easy to lose a game like this.
“We showed great character, at times a bit sloppy, but sometimes it takes one little switch and I think it was their second goal.
“It has been a long time coming, we’ve been one of the best teams in the world in the years we’ve been together, we deserve a trophy.
“But no one is going to give it to us, we have to keep pushing – and not just for us, but for the fans – we have to win something.”
Mourinho admitted that his side were outplayed on Wednesday but was delighted with the result.
“My team performance was in the limits. It was in the limits for me with players available and not available. It was in the limits for them because two days ago they played such an incredible match,” Mourinho told BBC Sport.
“We suffered. We played against a very good team, we played against a team that was the best team on the pitch but we deserved to win because we were in our limits. They had their best players, they had one more day rest, they were fresh.
“I think I did very well because I had to manage a team with so many difficulties. I changed from the back five to the back four in the moment when I could. Then Dele Alli became the link.
“The players [played with their] souls, and heart and gave absolutely everything. Four matches over two rounds, really hard for the boys. They deserve this happiness.”