The Bolton players were incensed when El Hadji Diouf's header moments before the half-time whistle was allowed to stand despite claims for offside against the Liverpool player.
But after viewing the incident Allardyce dismissed any thoughts that the decision was controversial.
"I know my players were upset, and there was a suspicion of offside, but I've now seen it on the replay and it was a very good goal," he admitted.
"The official was spot on, Diouf wasn't offside when Owen played his cross in. In fact Liverpool scored two very good goals."
"The bottom line is that neither side had many opportunities but Liverpool had the quality to take them and we didn't.
"We were close to them all day, but we can't turn our possession into goals. That's the difference between us and we paid the price.
"It's no good turning in reasonable performances without any end product. That's why we are fourth from bottom and they are where they are," he added.
Liverpool Match Report