The Sky Blues were involved in FA Cup action three days ago but eked out a result thanks to Carlos Tevez's late winner.
"I was not frustrated. It was a difficult game because we played three days ago and Wigan play good football," BBC Sport quotes Mancini as saying.
"We were so tired and didn't play well in the first half. In the second half we started so so but in the last 20 minutes we finished well."
The Italian also addressed the performance of Micah Richards, who recently returned from a six-month injury layoff, conceding that the right-back is some way short of full fitness.
"He's not in good form. Micah needs to work a lot, a lot, a lot because he played for 70 minutes but his form [has a long way to go]," he added.
The result leaves City in seventh place in the table, 13 points behind leaders Manchester United.