Manchester United fought back from 2-0 down with just three minutes remaining with goals from Paul Pogba and Victor Lindelof but it was a lucky escape at Old Trafford.
Burnley frustrated United throughout the 2-2 draw and became the first team not to lose to United since Solskjaer replaced Jose Mourinho in mid-December.
Since losing 3-1 to Liverpool in Mourinho’s final game in charge, the Red Devils had won six consecutive Premier League matches and two FA Cup ties.
And the Norwegian suggested the previous winning run caused United to become too relaxed early in the game.
“The performance wasn’t too bad if you look at it in the end, we had loads of shots, efforts, possession, we were just too slow,” Solskjaer said.
“We started the game almost feeling like the eight previous games meant we could start the game with a 1-0 lead, but it doesn’t happen like this.
“We have to earn the right to win the game by having a good start. They made it difficult for us, but then again we had a great comeback.
“The danger of winning might be that you think what we’ve done before gives us the right to start off on 90 per cent.
“But you have to start properly in each game, and today we didn’t start well enough to cause problems.”
Another three points against Sean Dyche’s men would have move United level on points with Chelsea and Arsenal in fourth and fifth spot respectively.
But it was not to be and Solksjaer was at least happy with the way that his players kept going right to the end and at least got something out of the game.
“That’s a big plus, that we find a way, because how they reacted was good, that’s a big plus for me,” he added.
“Me and Mick [Phelan] learned a lot today about the place, the players.
“I think all in all you’d be disappointed if you say you lost two points at home, but the reaction was good and I don’t think we deserved to lose the game.
“The decision-making could have been better at times, but that’s learning. If the game was two or three more minutes we could have got the last one as well.”