A 4-3 penalty shootout victory over Bayern Munich on the Germans' home ground after a 1-1 draw following extra time was the culmination of a stunning sequence of results.
Chelsea's first European Cup looked highly improbable when they trailed 3-1 to Napoli after a last-16 first leg but Di Matteo took over from the sacked Andre Villas-Boas and masterminded a comeback against the Italians and then wins over Benfica and, heroically, holders Barcelona.
Asked if Di Matteo should now get the full-time job, captain John Terry told ITV on Saturday: "Look at that trophy. We hope so. Robbie has been fantastic since he came in.
"It was a superb display from the whole squad. When our backs are against the wall we step up to the mark."
Goalkeeper Petr Cech, who saved Arjen Robben's penalty in extra time after Didier Drogba had equalised Thomas Muller's goal in the 90 minutes, echoed Terry's view of the former assistant coach.
"Whatever happens to him, he has got two fantastic cups. He has done enough to get the job but that is for the board to decide," said the Czech, pointing out Di Matteo also helped Chelsea beat Liverpool in the FA Cup final earlier this month.
Captain for the night Frank Lampard said Di Matteo had helped turn the club's flagging season around.
"It is not a question for this moment. He took us from a struggling team maybe going out of the Champions League and now we have won it, so just look at that," Lampard said.
The Londoners finished sixth in the Premier League, their worst placing for a decade, but the Champions League triumph ensured they would make next season's top European competition.
Media reports have linked Chelsea with former England manager Fabio Capello and neither Di Matteo and Abramovich have spoken publicly about the future.
"I'm enjoying this moment. I won't talk about it now," former Chelsea midfielder Di Matteo said.
