
The club's website reported that Mancini, 43, changed his mind late Wednesday after a meeting with club owner Massimo Moratti and said he was sorry about "the misunderstandings that may have arisen."
The Serie A title holders lost 1-0 at home against Liverpool on Tuesday night to go out 3-0 on aggregate in the round of 16. Minutes after the defeat, Mancini said he would quit his job at the end of the season, despite having four more years of his contract to run with Inter.
"Only president Moratti, all of Inter fans and our team can understand how it feels after missing a goal we truly wanted to achieve," Mancini wrote on the website.
"I hope that those who live football understand the outbursts and the bitterness of such delicate moments."
Beside thanking the president for his understanding, Mancini said he and the team are "ready to fight until the last minute, with great determination, to win our third (straight Serie A) title and to try and win the next Champions League."
Inter have a six-point lead on second-placed Roma with 11 games left to the end of the Serie A season and are also vying for the Italian Cup.
"After a storm like this, there is water around for some time, and it must be dried out," Moratti said. "So I think that Mancini should talk to the team. I think an explanation is needed.
"To me, he expressed his will to remain at Inter, not by force but with pleasure, through the end of the contract, unless someone changes mind. And for the time being this seems to be a happy solution."
Moratti, 62, changed 11 coaches in 14 seasons as club owner. He hired Mancini in 2004, renewing his contract last year on a salary of 6 million euros (9.35 million dollars) per season until 2011.