Nicklas Bendtner's second-half strike was enough to condemn the Merseysiders to a third successive Barclays Premier League defeat
O'Neill, who went into the game without suspended duo Lee Cattermole and Stephane Sessegnon and the injured Kieran Richardson, was delighted with a result which ended a three-game run without a league win and left them eighth, just two points behind Dalglish's men.
He said: "In a game of very few chances, it was great to get the goal and it eventually proved the winning goal in the match.
"With the changes that we had to make with influential players out of the team, I couldn't really have asked for much more. It was a great effort by the team."