It had been reported that the Manchester United boss had argued with the Portuguese midfielder during the 6-1 defeat to Tottenham in United's last match, although both parties have now denied the claims.
Solskjaer said: "It's one of those things that you have to get over as soon as you can and move on. We know any little chance from outside ... you want to create a division.
"I think Bruno spoke really well the other day about how we are united, we have to stay together. We can't listen to everyone outside. We've got to just get on with it.
"Bruno's now lost two league games since he came to the club and he came in February, but it's been two in quick succession.
"So, he's not used to losing league games for us but now, Bruno, welcome to Manchester United - this is what happens when you lost a couple, they're going to try to create a division between us.
"But that's not going to happen because this group is a group that wants to work hard together, stick together."
The Norwegian coach has also tipped Harry Maguire to bounce back from a wretched game for England as they lost to Denmark and he was sent off.
Solskjaer said: "Harry's got great resilience. I know he'll bounce back.
"I know that he wants to play, he wants to just work his way out of the last couple of games that he's been criticised [for]."