Solskjaer, right, and United are on a run of two straight victories after failing to win in their previous three
Ole Gunnar Solskjaer wants Manchester United to show equality on the pitch after the alleged racist abuse of some of their players during last Sunday's Premier League win at Manchester City.
A 41-year-old City fan was arrested after a video on social media appeared to show a man making monkey gestures.
"What we can do is go out onto the pitch next time and prove we are all equal," said United boss Solskjaer.
"This isn't how it should be in football."
Midfielders Jesse Lingard and Fred both appeared to be targets of abuse with the latter also hit by objects thrown from the crowd as he attempted to take a corner at City's Etihad Stadium.
"We have spoken with the boys of course," said Solskjaer. "It has been a tough couple of days for Jesse and Fred."
Manchester City condemned the abuse with Fred saying after the match that it is evidence that "we are still in a backward society".
"We are all the same regardless of skin colour, hair and gender," said Fred in an interview with ESPN Brazil.
"We came from the same place and we all go to the same place when it's all said and done.
"I have a lot of friends in the locker room who hugged me, like Lingard. I don't want to think about it. I just want to move on."
Still no date for Pogba return
Pogba will enter the final year of his United contract at the start of next season
Paul Pogba has not played for United since suffering an ankle injury in the draw with Arsenal in September.
The midfielder was initially expected to miss only two months, but his recovery was slowed by a setback.
Solskjaer admitted he was now not sure if the 26-year-old record signing would be back before the New Year.
"No. Too early," said the Norwegian when asked if Pogba could be involved in Thursday's final Europa League group match at home against AZ Alkmaar.
"We hope 2019."
United have already qualified for the knockout stages of the Europa League and will secure top spot in their group with a draw or better.
Analysis
BBC Sport's Simon Stone:
It has been 14 games and 10 weeks since Paul Pogba last played for Manchester United.
At recent news conferences, Solskjaer has been adamant Pogba would return at some stage during 2019.
Today that certainty wasn't there.
Instead it turned into 'hope'. Solskjaer has ruled Pogba out of Thursday's Europa League game against AZ Alkmaar. After that there are five more games left in 2019.
Rumours persist about Pogba's Old Trafford future and whether he will play for Manchester United again.
United officials continue to reject such talk but this won't make the speculation go away.
Source: bbc.com