Supporters calling for the removal of the Glazer family as owners broke into Old Trafford and surrounded the Lowry Hotel in Salford where the players were staying ahead of the game.
Clashes later in the day caused injury to 12 officers, according to the Greater Manchester Police, while investigations into damage at the stadium are ongoing.
"We wanted to play, we wanted to beat Liverpool for the fans. As I've said before, we have to listen and have to hear the fans' voice.
"It's everyone's right to protest but it has to be civilised and in a peaceful manner.
"Unfortunately when you break in, when police officers get injured, that's one step too far and unfortunately now when it gets out of hand like this it's a police matter, it's not about showing opinions any more."
United head to Italy with a 6-2 lead from the first leg and on the verge of reaching a first final since Solskjaer's appointment in December 2018.
They are also on course for a second place finish in the Premier League and Solskjaer is hopeful issues off the field will not disrupt the players in the final weeks of the season.
"My focus has to be on the results but you don't need to be a rocket scientist to see we have challenges and frictions," Solskjaer added.
"Other individuals than me have started already, discussing with fans, communicating with fan groups, which is going to be massive going forward.
"The players have done terrific to be where they are. I would be sad if all the good work players have done is disrupted. Our focus is on playing well and getting to a final."
The latest round of anti-Glazer protests -- simmering since their takeover in 2005 -- have been triggered by the failed attempt to join a European Super League.
After Sunday's demonstration caused the postponement of one of the biggest fixtures in the English football calendar, further protests are planned but Solskjaer said he does not want a repeat of the scenes over the weekend.
"It has to be in a peaceful manner," he said. "Our fans want a team that is attacking football, scoring goals, winning trophies so they can identify with them.
"We want to be a Man United team. My responsibility is results.
"Everyone has got a human right to be heard but it has to be peaceful. When you step out of line, break on the pitch, into dressing rooms, it's one step too far -- that's not nice."