Gareth Southgate's side triumphed 4-3 on spot-kicks after a 1-1 draw at Spartak Stadium, in which Yerry Mina's stoppage-time header cancelled out Harry Kane's opener from 12 yards.
Alli admits it was a major blow to concede at the death in regulation time but praised his team-mates for keeping calm before winning a World Cup match on penalties for the first time.
"When you concede such a late goal like that it can really knock you back," said the Tottenham midfielder. "But we didn't panic, we kept the ball, they didn't have too many chances after that and now we have to focus on the next game.
"We're confident in ourselves and hopefully we can go all the way to the final. We know it's going to be difficult, we've seen with other teams how difficult this World Cup has been. But we have to believe and we have to keep fighting and we have to get past Sweden first [in the quarter-finals]."
Kane's penalty was his sixth goal at the finals in Russia and made him the first England player to score in six consecutive appearances since Tommy Lawton in 1939.
"He's a world-class striker and he deserves it," Alli said of his Spurs team-mate, who leads the Golden Boot standings by two goals. "If he keeps scoring, we'll all be happy."
Alli also praised goalkeeper Jordan Pickford, who was criticised for his performance in the 1-0 loss to Belgium, for his heroics in saving Carlos Bacca's key penalty.
"It was a great save and he's a phenomenal keeper," he added. "Every man had to show his worth and Jordan Pickford definitely did."
England's triumph was their first on penalties at a major tournament since 1996 and saw them reach the quarter-final stage of a World Cup for the first time since 2006.
Kieran Trippier says the players focused on clearing their minds of past failures as they booked their meeting with Sweden.
"I couldn't be happier for the team and for the whole country, the fans, everyone involved," he said. "It's just an unbelievable feeling, the best feeling of my career.
"People go on about if England get to a penalty shoot-out we won't win but we really do block all that out. We just focus on ourselves. We know how much ability we have and we believe in ourselves.
"To be part of this team is an unbelievable feeling. Like I've said before, the spirit in this team is incredible. I love this team. We all feel the same, passionate about this team, we all want to do well."