Karanka criticised his players after the game for not showing any "fight" and said he had been embarrassed for the club's large away following.
Doncaster battled hard in the difficult blustery conditions and were the better side overall - especially in the first half.
More than 4,000 Boro supporters were among the 11,440 crowd and Karanka said: "It was difficult for both sides in the windy conditions.
"But when you can't play you need to fight and we didn't do that.
"When you don't play and you don't fight it makes it difficult to win the game and is an embarrassment for our supporters.
"We have a huge away following. People came to support us and we didn't play for them like we should.
"Doncaster were better than us at fighting for the ball and, in the circumstances, I'm happy to get a point.
"But I'm not happy with the way we played. You struggle to score goals when you don't play well.
"It wasn't a tactical problem and if we had performed like we are capable of then we would have won the game."
Chances were few and far between in the first half but Emmanuel Ledesma went close for the visitors after the break and Chris Brown missed the best chance of the match for Doncaster from close range on the hour mark.
Brown had a volley cleared off the line in stoppage time as the visitors' luck held.