The victory represents an incredible turnaround from their mid-season slumbers, which resulted in the sacking of Andre Villas-Boas. But interim manger Di Matteo never did feel his club's stalwarts were past it.
"We've had a difficult season and a lot of criticism," he said. "But the players responded to all the adversity we've faced.
"The answer was on the pitch. The football is always the best way to deliver the answer.
Di Matteo shrugged off suggestions that the permanent manager's job will be his reward for winning the FA Cup and taking the Blues to the Champions League final, saying that Roman Abramovich will make the decision in his own time.
"It's irrelevant," the Italian said. "The boss will make the decision and we'll respect it. The players will be fine.
"I am very fortunate person, so it's not an issue for me. I'll speak to him, don't worry. I speak to him in general."
Kenny Dalglish lamented his team's failure to turn up until late in the match.
"We were excellent for the last half hour, but the game lasts for 90 minutes," said the Scot.
"You can't give a team like Chelsea a two-goal head start.
"It's credit to our lads that they went close to an equaliser after Andy scored, but they had left themselves too much to do.
"I don't think the first hour was a reflection of the quality of the players we had out there but I don't know if that's was down to inexperience."
Chelsea's star man Drogba was thrilled.
"That's the reason why I came here, to win trophies and to make history with the club," he said.
"I'm very proud. I'm very proud of it, but I have to give credit to all my team-mates. During the last six years, I've been playing here all the finals, I'm really happy and I really want to thank them because they always put me in the best conditions to score goals.
"We made history, not only me. "The result is great for us, for the fans, for the club."
Liverpool defender Daniel Agger admitted that his side took little heart from their late fightback.
"It simply was not good enough for the first hour and we can only blame ourselves," said the Dane.
"We definitely were not good enough. Andy did really well when he came on and got a lot of balls to work with but sadly it was not enough."