But Emile Heskey's late goal gave all three points to The Reds, leaving Allardyce pondering over how Bolton didn't get at least a draw from the game.
"Every man was magnificent today," he said. "We just made some slight errors and Liverpool punished us heavily.
"After the effort to come back to 2-2 we got over-excited. We should have calmed down and got the ball as afar away from our goal as possible.
"To score two goals at home and not get a point is not acceptable. It's a great shame but we've got to take it on the chin.
"But at least we are looking a lot better defensively and attacking-wise as a Premiership unit. I hope that will stand us in good stead."