Chelsea midfielder Ramires gave his side the lead in the first half after he raced through down the right and fired past Pepe Reina in goal, before Didier Drogba clinically found the far corner to double their advantage right after the break.
On both occasions, the defending from Liverpool was far from ideal and Dalglish admits his side left themselves with a huge mountain to climb thereafter.
"With a team the quality of Chelsea you can't give them two goals start and expect to give yourself an opportunity to get something from the game," the Scot bemoaned.
"[We] were excellent for the last half hour but the game lasts for 90 minute."
After going two goals down, Dalglish threw on Andy Carroll and the England international had an immediate impact, pulling one back for the Reds before powering a header towards goal that was tipped by Petr Cech against the crossbar and back out again.
Despite protests from the Reds camp, the ball was deemed to have not completely crossed the line and the Liverpool boss believes the match officials deserve praise if the decision is proved to be the right one.
"I've not seen it on television but somebody said sometimes you get it and sometimes you don't," he added. "This time we didn't get it.
"If the officials have got it right I hope they get the credit they deserve for it."
The Reds then spent the remainder of the game banging on the Chelsea door but were unable to find a way through, and while Dalglish was pleased with they way his players responded, he conceded it was too little too late.
"It is credit to the lads that they went close to getting an equaliser after big Andy scored, but we left ourselves too much to do and I don't think the first hour was a true reflection of the quality of the players."