The Clarets silenced Old Trafford by taking a 2-0 lead. However, in typical United style, the Red Devils fought back to salvage a point.
Solskjaer blamed United's slow tempo on the result saying: "We fought, that wasn't the problem. We were just too slow in possession in the first half.
"For the first goal we played our way into trouble. It wasn't the attitude, the application was too slow and the tempo on the ball wasn't good enough. But the reaction was good."
Despite not getting the win, the manager was pleased to see his team show great character in the final five minutes of the game.
He said: "The comeback was brilliant, the players have been asked about how they would react if they went 1-0 or 2-0 down so I felt the comeback was fantastic.
"We had loads of chances, loads of possession, we didn't deserve to lose. But we did it to ourselves really.
"We disappointed ourselves and we disappointed the crowd today, but the ones who stayed had a typical Old Trafford finish to the game so that was a big plus."