"It was important to start with a victory, but we relaxed on 3-0 and that was a mistake," Mancini told Inter's website on Sunday.
"All goals are important, especially when they are decisive for the result."
Inter managed to keep their lead ending the game in a 3-2 win, but for Mancini the win isn't enough.
"We did very well for an hour but then we thought we had won the match and this was a mistake because a goal can reopen the match at any time and give your opponents confidence and momentum," the coach said.
Though Mancini allowed for exhaustion, admitting many players weren't in top form after featuring for the national team, he felt the team deserved the win.
"Over the whole game, we deserved the win. Fiorentina were a huge obstacle and, even with the 19-point penalty, will remain a difficult opponent for anyone this year," he said.
Argentinean Esteban Cambiasso scored a double and made the third for Zlatan Ibrahimovic before Luca Toni struck twice.
Mancini was quick to praise Cambiasso's performance.
"Cambiasso did very well and he showed again tonight how perfectly he gets into spaces," he said.