United endured their eighth goalless draw of the season at Leeds, where tensions threatened to boil over when Maguire bit back at advice from Fred in the 72nd minute.
Maguire could be heard calling Fred a ‘f—–g idiot’ during a stoppage but Solskjaer said United do not just want a squad full of ‘nice guys’.
“We have got a group that demands a lot of each other,” Solskjaer said of the quarrel. “The standard is high, both in training and the game.
“It’s not just about being a nice guy and cajoling. We demand maximum effort.
“I was really proud in the second half how strong we looked, how we dominated the possession, the regains, how quickly we won the ball back and never felt they threatened our goal in the second half.
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“But we missed a little bit today, an extra spark to win the game.”
Despite dropping two points, United are unbeaten in their last 24 Premier League away games and are two away from going the whole league season unbeaten.
United travel to Aston Villa next month and their final game of the season is at Wolves, where they have not won since the Midlands side were promoted back to the Premier League in 2018.
“It’s a good achievement, no matter if there are fans or no fans,” Solskjaer opined. “Twenty-three or 24 games without defeat.
“I think the players have prepared well for these games, we travel, the work by the coaches every game is really good, is planned down to a tee and I’ve got to say we hope it continues.
“Because we’ve got big games coming up and we want to take as many points as possible.”
United host Roma in their Europa League semi-final first leg on Thursday before Liverpool visit on Sunday.
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