The managers had a tense verbal exchange following Dirk Kuyt's equaliser a full 11 minutes into stoppage time, before eventually shaking hands after the final whistle.
A minimum of eight minutes were added on by referee Andre Marriner at the Emirates following Jamie Carragher's head injury, and Robin van Persie slotted a penalty at the end of those after Cesc Fabregas was felled by Jay Spearing.
But Wenger was furious that Marriner allowed another three minutes of play after the goal and even angrier when Emmanuel Eboue was deemed to have knocked over Lucas in the box.
Wenger revealed later he told Dalglish it "was not a penalty" as they came together, a statement Dalglish reacted to angrily. The Liverpool boss appeared to tell Wenger to "p*** off" as he turned away in disgust.
Wenger, who confronted the officials as they left the pitch after the match, explained his side of the story: "All I said to Dalglish was it was not a penalty. You can check with TV to see what I said. We conceded a penalty after 11 minutes when the referee said there were eight minutes of injury time. I don't see where those three extra minutes came from and it was no penalty. Eboue goes for the ball - not the player. But Lucas stopped in his way in front of him."
Dalglish looked to move on from the incident as quickly as possible, instead focusing on the resilience of his injury-hit side.
"I just told him there I still owe him dinner," he said. "There's no problem. I don't want to repeat what was said. It would be very sad if that was allowed to overshadow what my players have achieved out there."
He added: "In my opinion there was one correct penalty decision and one incorrect one. Work it out for yourself which was which... I was disappointed when Arsenal were awarded that penalty so late in the game - but if that's what is given then you can't dispute it."