The Serie A club go into Wednesday's Coppa Italia quarter-final against Napoli licking their wounds after back-to-back league defeats.
The most recent setback came against Sassuolo, prompting angry confrontations between players and fans afterwards - involving most notably striker Mauro Icardi.
After Inter fans threw players' shirts back from the crowd, the Argentine reacted angrily and Mancini told reporters on Tuesday his team needed to accept flak that comes their way.
"Icardi made a mistake, because we need to accept criticism," the Italian explained.
"I told him he shouldn't have gone to the stands, because it was only to be expected that the fans would be angry.
"Having said that, the Inter fans have always stuck with the team and I'm sure they'll continue to do so.
"The lads need to have a big-club mentality and that's what they're doing but what's clear to all is that we're making too many mistakes at the minute.
"I always knew there would be some difficulties in terms of changing the playing system and mentality after two years, but I’m happy with how the squad is doing.
"We need to arrest this trend, score more goals and try not to concede."
A semi-final against Lazio awaits the winners of Wednesday's clash, with Rafael Benitez's Napoli having lost just once since the turn of the year.
"Anything can happen tomorrow – the gap between us and Napoli in the league is irrelevant," Mancini added.
"We hold the Coppa in high regard and want to perform well."
