"I think they started better than us but we were the better team at the end," said Dalglish.
"It was fortunate for us we got the equaliser as quickly as we did, it kept the spirits up. We tried our very best to win it in the second half but unfortunately we just could not get it over the line."
City, who had won their last seven league games but went to Anfield after losing 2-1 to Napoli in the Champions League in midweek, started the better team but were left hanging on to a point at the end.
Manager Roberto Mancini was satisfied with a draw on his 47th birthday but added Balotelli should not have been sent off.
"It's a good result for us because we played with 10 men for the last few minutes," the Italian said. "But for me the second Balotelli foul was not a yellow card, he didn't deserve it."
Liverpool's Charlie Adam celebrates after his shot was deflected into the goal by Manchester City's Joleon Lescott
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