The defending champions ended a run of three Premier League matches without a win at the KC Stadium on Saturday, but it could have been a different story as City were pegged back by half-time despite taking a two-goal advantage after just 11 minutes thanks to goals from Sergio Aguero and Edin Dzeko.
Mangala was at fault for both Hull goals, first heading into his own net before conceding the foul on Abel Hernandez which allowed the striker to equalise from the penalty spot.
In the end it mattered little as Dzeko scored his second with a left-footed drive in the 68th minute, before Frank Lampard made it four goals in his past three competitive outings late on.
Speaking after the match, City boss Pellegrini was quick to absolve Mangala of any blame for costing City the goals and stated the close-season signing will continue to improve.
"These things can happen," Pellegrini said. "We started very well. We were very unlucky with two individual mistakes through the game.
"He [Mangala] was very unlucky with the own goal and after that he arrived late for the penalty but we continue to trust him because he is a very good player who had very bad luck.
"He's a very good player he will continue to play, he was a very good signing."
Pellegrini switched to a diamond formation by introducing Jesus Navas for Fernandinho in the 66th minute and the Chilean believes that the attacking risk proved crucial.
"I think it was important [to change] because we needed to continue working both wings," he said.
"We were drawing 2-2 at that moment so we had to take a risk, leaving Yaya [Toure] alone in that position with Navas and [James] Milner on both wings and David [Silva] free behind the strikers.
"We had to take some risks in some moments, and in the moment we scored we returned with Frank Lampard to the way we normally play. But it was important for the team to have some change."
