After taking in their manager's words, the Red Devils would eventually prevail 1-0 at Turf Moor through Paul Pogba's strike, sending them to the top of the table.
United could have been a man up in the first half after Robbie Brady appeared to deny Edinson Cavani a goalscoring opportunity with a foul outside the box, but after a video review, referee Kevin Friend disregarded Brady's foul entirely and instead called United defender Luke Shaw for an earlier challenge, issuing the left-back a yellow card.
United defender Harry Maguire then appeared to score the opener with a header, only for the goal to be called back due to a controversial foul by the defender during his leap.
Solskjaer admitted that his players were upset with the referee's decisions and needed to be calmed at the break.
"You've got to calm them down at half-time because emotions are running high because they disagree with the things that happen out there," Solskjaer told Sky Sports.
"So we have to take back control and we played really well in the second half and we held out at the end."
On the two incidents, Solskajer added: "I've not watched any of the decisions so I can't really say. Might've been a foul by Luke apparently so that's probably the right decision, definitely not a foul for Harry for his goal. If you can't jump and head it in like this, I don't believe that's anywhere near a foul. Delighted with the response after a bit of a tough first half-hour."
Pogba eventually found a winner in the 71st minute, with Solskjaer saying the France star is finding his best form after a difficult spell earlier in the season.
"I've always said Paul is a big player for us, he's a good character in the dressing room, he's someone the lads look to, he's a world champion," Solskjaer said.
"We're seeing the best of Paul at the moment – he's been injured and he's had Covid so it's natural to need to get back to fitness after that."
Solskjaer also said he was looking forward to Sunday's table-topping clash with Liverpool, who are three points behind his side in second place.
"Of course we know we're going to the champions. They've had an unbelievable three seasons so we're ready for it," Solskjaer said. "But we're ready and we're excited, we're hungry for it and it's a test of character and quality again. We're in a good position going into it."