The Ivory Coast midfielder was brought off at the break after an out-of-sorts performance as the visitors played out an uninspiring stalemate at Swansea with Wembley a week away
The visitors were second best in the first half and the Italian replaced Toure at the break with what appeared to be a tactical change after a lacklustre opening period from the midfielder.
Mancini, however, confirmed the Ivory Coast international had a problem before the game but believes he should be fit for next Saturday’s Wembley showdown with Wigan.
"Yaya Toure was not good, he had a problem in the warm up and when he came off we missed him,” he told BBC Sport.
“He will be OK for the final though.”
The game had all the markings of an end-of-season fixture where neither side had much to play for, but the City boss was disappointed the likes of Edin Dzeko and David Silva wasted excellent chances to win the game.
"The first half was so-so but we missed five incredible chances to score,” Mancini added.
“We had motivation because we want to get second place.
“Before the FA Cup final we have another important game, we need to win on Tuesday and then we will prepare for Wigan."
Swansea manager Michael Laudrup, meanwhile, admitted it wasn’t the most high-quality affair at the Liberty Stadium but was disappointed his side had a strong penalty appeal turned down for a foul on Michu by Matija Nastasic.
"We were playing a great team, but the second half was not the best football for both sides,” he told BBC Sport.
"We keep our position of ninth in the table with a game in hand so we are happy with that. Michu was fouled in the first half, it was a huge penalty but we have not had one in the league all season."