But having strongly criticised Shaw after leaving him out of the squad for Saturday's 0-0 draw with West Bromwich Albion, Mourinho again took the 21-year-old left-back to task.
"He had a good performance, but it was his body with my brain," Mourinho told reporters at Old Trafford.
"He was in front of me and I was making every decision for him.
"We need at this level the fantastic body to play football, but he cannot play (by relying on) my understanding of the game.
"He must understand, he must think, he must accelerate the process. He is 21, he is old enough to have a better understanding of the game. But today he has with a positive feeling."
Phil Jagielka's 22nd-minute opener looked poised to condemn United to a first defeat in 20 league games.
But deep into stoppage time Shaw's shot was handled by Ashley Williams, who was sent off, and Ibrahimovic converted the equaliser from the spot on his return from a three-match suspension.
Mourinho's side have scored just once from 36 efforts at goal in their last two matches and the manager is demanding a better conversion rate.
He admitted that striker Marcus Rashford, without a league goal since September, is short on confidence.
"It's easy to see in the kid," Mourinho said. "He is desperate. He tries. It's not a surprise for me. The second year after the first one is difficult.
"It's something I will try to find if it happened with Ryan Giggs, if he appeared as a kid and then the next year was not the same. The kid (Rashford) is phenomenal, an amazing professional."
- Mirallas angry -
Reflecting on a result that left United four points off the Champions League places, Mourinho said: "Twenty matches unbeaten is amazing.
"In the modern Premier League, it's very difficult to do it. But we need to score goals to win matches.
"We almost lost the game against West Brom because of a bad mistake. Today we almost lose the game because of a bad mistake.
"There is not one match at home that doesn't have emotion because we go until the end and we try and we change system and we try. But we don't score enough goals."
Everton manager Ronald Koeman was left to rue his side's failure to score a second goal with a couple of promising second-half counter-attacks.
Koeman had no complaints about referee Neil Swarbrick's decision to give United a late penalty and send off Williams, but he did feel his team should have secured all three points.
"We lost two points because we did a really good job tonight. We controlled the game," he said.
"Maybe in the first 10 or 15 minutes, United were the better team. But we controlled the game well, defending well.
"We have to score the second. Even not scoring the second, I was comfortable because I know we need to defend.
"It's difficult with Zlatan, Marouane Fellaini, Paul Pogba in the box, tall people. But we were well organised.
"The penalty, it's hard to take. It's the right decision, but one minute and you win the game.
"It's painful, and it's difficult for the boy Williams because he had played well. But if you can't win, don't lose."
Koeman indicated that he would speak to forward Kevin Mirallas, who reacted angrily to being substituted midway through the second half, refusing to shake the manager’s hand.
"I can understand players if you substitute them that they are a little disappointed," Koeman said.
"That's not how you react and I will speak about that with him."