Dominic Calvert-Lewin turned home Lucas Dignes free-kick with the last action at Old Trafford.
Ole Gunnar Solskjaer was frustrated by the way Manchester United blew victory against Everton after conceding with the last kick of the ball.
Just days after thumping nine-man Southampton 9-0, the Red Devils were on course for another Old Trafford victory having recovered from a poor start to the second half.
United went into half-time with a two-goal cushion thanks to Edinson Cavani’s header and a sublime Bruno Fernandes effort, only for Abdoulaye Doucoure and James Rodriguez to draw Everton level within seven minutes of the restart.
Scott McTominay put the hosts back ahead, only for Dominic Calvert-Lewin to react quickest when Lucas Digne’s stoppage-time free-kick was flicked on to seal the Toffees a 3-3 draw.
“Well, of course when you’re in the 94th minute and you’re winning the game I think it feels worse, when you concede in the last minute,” Solskjaer said.
“The first five minutes of the second half, of course, they were hard to take but the rest of the second half we played some good football and we should have been out of sight, really.
“Football is about getting the ball into one net and keeping it out of the other and we didn’t manage to do that. We didn’t manage to keep it out.
“That’s what cost us because we played some very, very good stuff.
“You know, you can sit and you can talk about the good performance or the domination of possession and chances we had, but still we come away with only one point.”
The equaliser came after Everton exposed United’s all too familiar frailties from set-pieces, with Michael Keane flicking on Digne’s free-kick and Calvert-Lewin turning home.
“We know that many teams in the Premier League have got good players and Everton more than others,” Solskjaer said.
“When we give them a chance to even put the keeper up there, there was 10 men in there – just one that launched it and 10 in the box.
“It’s about staying high, winning the first challenge, of course. If you don’t stay up on the line and clear it, and we just couldn’t manage.
“But it happened before that. We should have played the minute out better. Of course we should have.”
Solskjaer says Paul Pogba will have a thigh complaint scanned on Sunday after limping off in the first half of a match that Everton boss Carlo Ancelotti felt his side began too tamely.
The Italian could not have asked more of his players after the break, though, as they kept going until the death.
“I’m very pleased,” Ancelotti said. “I think at the end of the day we didn’t deserve to lose.
“It’s true that the first half we were a little bit shy but I think that we didn’t deserve to be down 2-0.
“Of course the second half it was a different game, different courage.
“I think we were a little bit shy in the first half and we could create more problems in front using the counter-attack because the first 20 minutes, until the first goal of Manchester United, we were in the game as we wanted.
“We didn’t change the tactic, the strategy (at half-time). We had the same but with more courage.
“I think the first goal that we scored we built up from the back properly as we wanted to do and did what we didn’t do in the first half.
“It was a good performance. I think, of course, when you score in the last second of the game we were a bit lucky, to be honest, but I think we deserved the luck.”