The Blues' hopes of finishing third or fourth looked doomed after Wednesday night's defeat to Newcastle that left them four points adrift with just two games remaining.
But the Magpies' loss to Manchester City and Tottenham's draw at Aston Villa on Sunday - coupled with Arsenal's failure to beat Norwich on Saturday - kept alive sixth-placed Chelsea's slim hopes of qualifying for next season's Champions League via the Premier League.
They must beat FA Cup final opponents Liverpool for the second time in four days to stand any chance of overhauling two of the three teams directly above them.
Mata said of the clash at Anfield: "We have to win and still believe in playing the Champions League next year."
Mata said: "It's a hard stadium to play away at.
"Liverpool showed they have a great team and they are dangerous at Anfield."
Mata insisted there was no chance of him suffering burnout ahead of what could be more overtime for the winger on Tuesday night.
The 24-year-old had looked set to be handed a well-earned day off at Anfield following Chelsea's FA Cup final triumph, having been through a punishing run of fixtures.
Caretaker manager Roberto Di Matteo admitted after Saturday's Wembley win that his line-up for Tuesday would depend on the outcome of Sunday's games, implying that were a top-four finish mathematically impossible he would make wholesale changes with the May 19 Champions League final in mind.
But he would have been pondering on Tuesday whether to field his strongest possible side - which would surely contain Mata, who is the only outfield player to have featured in all 18 of his matches at the helm.
After winning the FA Cup in his maiden season in English football on Saturday, exhaustion was the furthest thing from Mata's mind.
"I have plenty of energy left," said the Spain star.
"It is a long season and my first in England, but the benefits of winning easily outweigh the fatigue."
Tuesday's fixture is arguably one of the toughest Chelsea could have faced after beating Liverpool on Saturday.
Kenny Dalglish's men will be desperate for revenge and to make amends both for their Wembley defeat and one of their most miserable seasons at Anfield in the club's history.
But Frank Lampard insisted this evening's game would have been harder if Chelsea had lost on Saturday.
"Less difficult than losing, without a doubt," he said, referring to the respective confidence both sides now have as a result.
Defenders David Luiz and Gary Cahill are both set to miss Tuesday night's game due to hamstring injuries, with midfielders John Obi Mikel and Raul Meireles also sidelined for the Blues.
Luiz was confident of training fully ahead of the Blackburn game, acknowledging it was vital he and Cahill were fit for Munich, with John Terry and Branislav Ivanovic both suspended.
"Of course, I think it would be better for me and for my fitness, for the team, if I come back before the final," Luiz said.
"But I don't need to do it too quickly - I need to be intelligent.
"I have to come back at the right moment, not before.
"I know my body, I know I am feeling good, and that will form part of the decision."