Solskjaer since taking charge at Man United is yet to convince many football fans as results have been inconsistent at Old Trafford.
Speaking on Monday Night Football, Carragher who now works as a pundit after his football career urged Man United fans to accept that Solskjaer is not capable of competing with the top managers in the game.
But Solskjaer is not bothered by the comments from Carragher.
"No it doesn't affect me. Of course you see comments once in a while, I didn't know what he was saying now.
"Of course we have got Liverpool on Sunday as well, so Jamie is always looking at these little things.
"I have got my values, I have got my way of managing.
"I believe in myself and as long as the club believes in me, I am pretty sure Jamie Carragher's opinion is not going to change that...
"You can see the progress, improvement, development and this season we still want to improve.
"Yeah, we’ve signed some players that have raised expectations. Other teams have signed players and improved as well so we’re in the same boat as all the top teams. There’s pressure all the time.
"There’s pressure on me, of course, but we’ve been through this before and we’ve come through it stronger as individuals and as a team."
