Liverpool started the brighter side as £25m signing Adam Lallana posed a threat, whilst Italy international Mario Balotelli missed a couple of half-chances.
They get their point and we are happy with the performance, if not the result
However, it was Steven Gerrard, recently criticised for a string of below-par performances, who broke the deadlock with a powerful free-kick in the 65th minute.
The Reds appeared destined to see out a third league win of the season and Balotelli was denied by the woodwork – but Jagielka popped up with a long-range strike in added time.
“The players were brilliant. We were clearly the dominant side in the game, but sometimes you don’t get what you deserve in football,” Rodgers told BBC Sport.
“But for a wonder-strike at the end of the game we would have got the three points.”
Rodgers added: “Balotelli should have scored. There was a touch on it [his shot] but I think he will think he should have scored. He had some exceptional touches in the game.
“We should also have had a penalty. If the Gareth Barry handball was not a penalty then you won’t see any penalties all year.
“But they get their point and we are happy with the performance, if not the result.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news