The Reds were abysmal in the first half at Bramall Lane and were fortune to only be behind to John Fleck's strike.
Solskjaer admitted he was angry at half-time and his mood would not have improved when Lys Mousset doubled the hosts' lead early in the second half.
However, the Norwegian took some comfort from a sparkling seven-minute spell his side produced to turn the game on its head as goals from Brandon Williams, Mason Greenwood and Marcus Rashford had the Reds in front with 79 minutes on the clock.
Solskjaer was denied a sixth victory in the last seven matches by Oliver McBurnie's last-minute equaliser but he believes he and his players can take some positives from what had been a dire situation.
"It was a very poor performance. I'm thinking back to Everton last season - that team gave up and this team didn't. So when we turned it around it's a great response to get from the boys," said the United boss.
"We did play badly in the first half. We didn't win any challenges, we weren't first to the ball, we didn't stick to what we had planned. I could have changed all the players at half-time, except David (De Gea) as he kept us in it.
"You don't expect them to give up, but last year we did. Today we didn't. Even though the big part of this game is a negative and we are disappointed with it, the overriding feeling is a positive because of the character to stick in there and turn it around.
"I was angry, disappointed at half-time. I had to wake them up. We had to go for it in the second half. We lacked desire in the first half and they had it. You've got to earn the right to win the game and we didn't have any right to win the game after 70 minutes.
"But the boys will have learned a lesson from the 71st minute to the 90th, or whenever they scored. You must remember that these players are young. The first goal gave them belief.
"It's not desire in terms of the word desire, maybe it's confidence in themselves. I don't doubt them wanting to win, sometimes young players don't really know how to win challenges like this and we must have learned a lot today, I'm sure we have.
"They've come through the academy most of these boys and in the academy you don't play in these kind of games, despite trying to teach them to play without fear, and they will have learned a lot in this 90-odd minutes - so there will be some pluses as well."
Sheffield United boss Chris Wilder was left to rue the seven-minute spell that turned the match in the visitors' favour. However, he was also pleased with the way his team responded to that disappointment by striking back to earn a point.
Wilder said: "Can we forget about that period, please? We just dropped off our energy levels. The old saying '2-0 is a dangerous scoreline' turned into 'oops, we're 3-2 down'.
"And you've got to give them credit, just as you have us with the way we fought ourselves back at the death to get ourselves something out of the game.
"It just flicked a switch for them when they got back into the game at 2-1, with what, from our point of view, is a goal out of nothing.
"No disrespect to the level we have come from, but we are talking Daniel James, Anthony Martial and Marcus Rashford and when they say yes, which they did, then the momentum and the scoreline dramatically changed.
"I would have been really disappointed had we not got anything from this game because for the majority of the time we were right up there in terms of the performance levels."
Fast Results
Scores
Racecards 
