Liverpool captain Steven Gerrard had given the hosts the lead with a free-kick in the 68th minute of the English Premier League match.
And Dalglish, who returned to the managerial hot seat at Liverpool in January, considers it is a sign of the advances his side have made that the players were downbeat after being unable to seal victory over the Premier League champions.
"We could have had all three points after what I think was pretty even and sterile beginning to the match," Dalglish said.
"I think it's a real indication that the players were disappointed in the dressing room after the match about drawing with a team like Manchester United. That shows how far we have come."
Manchester United manager Sir Alex Ferguson considered a draw theright result, not to mention an improvement on his team's poor record from their recent visits to Anfield.
"If you forget the last three games here and just focus on the context of today’s game, I believe the result is a fair one," Ferguson said.
"You can never be completely confident a goal will come when you are 1-0 down with 15 minutes to go but we do have the players who can come on and do that."
"It was a typical United v Liverpool game. They are always very intense, but I don’t think the game really started until Liverpool scored. Once they did, I think it was a very good game after that."
Much was made of Ferguson's decision to leave out Wayne Rooney and field Phil Jones as a defensive midfielder, with only one striker up front for United.
Dalglish was unconcerned about the unusual line-up his side were confronted by when the squad lists were handed in.
"Their team selection was not a surprise," he said.
"I think it was a compliment to us as well."
"Fergie always changes his team after an international break and they have got an important game on Tuesday. I've always said it's a squad effort and obviously Sir Alex thinks the same way."
soccerway.com
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