Marco Silva declared that Fulham will “go for it” in the second leg after Liverpool came from behind to win 2-1 in the first leg of the Carabao Cup semi-final.
Willian put the visitors ahead at Anfield before goals from Curtis Jones and Cody Gakpo.
It means Liverpool will take a lead into the return leg at Craven Cottage, but Fulham still have a fighting chance of reaching Wembley.
Whites boss Silva said: “The tie is still tight. We’ve lost the first half, so we’re going to have to go for it in the second at Craven Cottage.
“We have something to play for, clearly. We know what Liverpool are capable of with their quality, but the belief that we had before tonight’s game and the trust we had in ourselves to fight for it doesn’t change now the game is done.
“We have a tough game coming up against Chelsea but after that we’ll have good time to prepare for the second leg.”
Fulham frustrated the hosts during the first half and went ahead when Virgil van Dijk failed to deal with a ball into the box and Andreas Pereira teed up Willian, who showed great footwork to evade a couple of challenges and fire home.
Winning the away leg would have been a fantastic result for Fulham, who battled hard to protect their lead and were unlucky to concede an equaliser when Jones’ shot went in via a huge deflection off Tosin Adarabioyo.
And after good work by Diogo Jota on the left, Liverpool quickly netted again.
Jota found Darwin Nunez, who pulled the ball back for fellow substitute Gakpo to score with a first-time finish.
Liverpool continued to attack and three late saves by keeper Bernd Leno to deny Nunez could yet prove to be crucial.
“It’s not over yet,” said Liverpool boss Jurgen Klopp.
“I didn’t expect a result where we could book the hotel. We couldn’t do more than win the game and I’m absolutely happy.”