Bruno Fernandes scored twice after Bernard opened the scoring for the Toffees before Edinson Cavani caught his first for his new club to put the result to bed.
But with United one goal, there was a potential case for a penalty after Pickford smashed into Maguire.
Steve McManaman was convinced the incident warranted a kick in the co-commentary for BT Sport.
However, VAR decided to uphold Paul Tierney’s on-court decision to ignore him.
And Maguire is now out and in agreement with the referee, stating that it would have been a soft penalty.
“I just explained that in there, personally I don’t think it was [a penalty]“Said the Red Devils captain.
“I think maybe I fouled Jordan first. I put a hand in his chest when he went to catch the ball and felt a touch on my knee.
“I felt like I had probably pushed Jordan before and I know everyone is probably trying to jump on him by dropping the ball, but I felt like I was pushing him.
” I would say [a penalty] would have been a little soft.
The result is a huge sigh of relief for Ole Gunnar Solskjaer, who was under pressure following the losses to Arsenal and Istanbul Basaksehir.
And Maguire has admitted he’s hoping United have turned a corner.
“Sometimes it’s tough for the guys, but today we reacted really well to two bad results,” he added. “We felt like we were on the right track after [the 5-0 win versus] Leipzig but we felt like we let down against Arsenal.
“Another day Arsenal could have been a different result.
“It was a tight and nervous game, but we don’t want it to be tight and nervous when we play at Old Trafford.
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“We want to dominate the game. We gave them a soft goal and they won the game.
” During the week [against Istanbul Basaksehir] again we gave them a soft target to take the lead and we struggled to create any chances to come back.
“We knew it was an important game to come here and get three points. The boys reacted very well, but as we know, this is just the start.