Sergio Aguero fired the winner in the Dragon’s Den after Mario Balotelli, back from his four-match ban, forced an own-goal equaliser to cancel out Silvestre Valera’s 27th-minute opener.
Mancini’s men now start firm favourites to finish the job in next Wednesday’s second leg at the Etihad for a place in the last 16 against Legia Warsaw or Sporting Lisbon, who drew 2-2.
The Blues boss said: “We played a good game. The first half we had three or four chances and we were unlucky, but in the second half we played very very well.
“The second half, I told them only to play as we know how. Maybe we played higher (up the pitch) but we had seven or eight chances to score - and we didn’t give any chances to Porto, which is important because they are a top team.
“I think we are maybe 60 per cent likely to go to the next stage. But we’re playing Porto — they’ve shown they are a top team and it will be another difficult game in Manchester. We have to show the same concentration we showed tonight.”
Mancini added that he had not heard any racist chants, following unconfirmed reports that abuse had been directed at Balotelli, who made way for Aguero 12 minutes from time.