The Premier League champions were booed off at half-time against Swansea even though City eventually triumphed 1-0.
This came after their UEFA Champions League failure at Ajax, but Mancini admits that it is easy to forget they are sitting just a point off top spot in the Premier League.
"They must understand it was a difficult occasion," said Mancini.
"When you're tired and have just had a defeat in the Champions League, maybe you can be disappointing. All teams need their supporters for 90 minutes.
"This was a good win. After a defeat in the Champions League it was important to win quickly again.
"After all that's been said in the last few days, I thought we were bottom of the Premier League. But I've just looked at the table and we're in second position."