Inter looked to be in command after goals from Mateo Kovacic and Mauro Icardi gave them a 2-0 lead in Sardinia, only for Cagliari loanee Samuele Longo to pull one back in the 74th minute against his parent club to set up a tense finish.
But Mancini's men held on to claim a third straight win and move up to sixth in Serie A, four points adrift of fifth-placed Fiorentina, who they play on Sunday.
And the former Manchester City boss believes thoughts about that clash and the UEFA Europa League last 32 second leg with Celtic on Thursday may have caused his players to lose focus.
"If we don't make things difficult for ourselves, then we wouldn't be Inter," Mancini told Sky Sport Italia.
"We had the chance to score twice in the first half and failed. We went in front, then Longo came on and did very well. He used Juan Jesus' body to turn and deserves applause for a great goal.
"In the 10 minutes after that goal, anything could've happened. It was wide open and after 65 minutes we should've been well in control.
"When 2-0 up it's possible the team relaxed a little, especially with three intense games this week and not much squad rotation."
On-loan Arsenal striker Lukas Podolski missed a host of first-half opportunities for Inter, however, Mancini feels the Germany forward will make a key impact at some point this season, despite failing to find the net thus far.
"I believe the time will come when Podolski will score an important goal," he added. "Of the three in the first half, he usually gets at least one in. He's unlucky at the moment, but it will pass."
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