The Azzurri qualified for the Euro 2020 semi-finals where they will face Spain in London, with goals from Nicolo Barella and Lorenzo Insigne.
Italy had cruised through Group A with a perfect record, before beating Austria in extra-time and now one of the title favourites, Belgium.
“We’re not setting ourselves limits. We want to do the maximum,” Mancini told the post-game news conference.
“There’s still a long way to go, there are two games left and we will see what happens.
“We deserved to win. The players produced an excellent performance.
“We only suffered in the last 10 minutes and that was because we were really tired, we had given a lot. But we could have scored even more goals.
“We’ll enjoy this win before we think about Spain. I congratulate my lads, who were superb. I was sure we were going to play really well.”
Meanwhile, Belgium’s quarter-final exit leaves doubts about manager Roberto Martinez’s future in the role.
“As I say, at the moment, it’s still too raw and I do not want to say anything that it could be (seen as) emotional,” Martinez said.
“At the moment, all I want to do is look back into this tournament and I would say that the players have done nothing wrong. It is the opposite.
“They did everything they could to get us as far as we can. And now is the time to analyse and to assess. But, at the moment, the feelings of disappointment and sadness, unfortunately, is what is in my head now.”