The 33-year-old England captain scored his 100th league goal from the penalty spot three minutes before the break as the Reds twice came from behind to claim a point in a 2-2 draw with the 10-man Magpies.
Rodgers later saluted Gerrard, who led his country to qualification for the World Cup finals in Brazil during the international break, and predicted there is still more to come.
He said: "It's a monumental contribution. I have watched him play for many years as a young player and probably for me, his best Premier League goal came at this ground when he played against Newcastle.
"He scored an absolute screamer here from a free-kick. But he's an incredible player and I am fortunate enough that I get to know him as a man as well.
"As a captain, he has been brilliant for me. He understands the manager's role and respects it.
"He is a great player who has got many more goals to come as well. You see his fitness level - people talk about him and his fitness and how is he at 33?
"Well, he's played two really tough international games, played at a high level and he has also got a really good performance in, so he is still fresh and looking very, very good."
A thrilling encounter lifted off after 23 minutes when Newcastle midfielder Yohan Cabaye smashed a dipping 30-yard shot across goalkeeper Simon Mignolet and inside the far post.
However, the Reds were back in it before the break when central defender Mapou Yanga-Mbiwa hauled back Luis Suarez inside the box and referee Andre Marriner, for the third successive time in a Newcastle game, produced a red card.
Newcastle boss Alan Pardew said: "I thought it was a tough call. I don't think Mapou really pulled him down in a manner that was a definite sending-off.
"He got a little piece of him, he was the last man and I suppose by the letter of the law, he had to go. I haven't got a massive problem with it."
Gerrard calmly dispatched the resulting penalty and the visitors looked to be set fair.
However, substitute Paul Dummett, a home-grown left-back who had been asked to plug the gap in central defence, turned up at the far post 12 minutes after the restart to side-foot home a Cabaye free-kick and restore the Magpies' lead.
Liverpool laid siege to the home goal and finally got their reward 18 minutes from time when Daniel Sturridge headed Suarez's cross past keeper Tim Krul, and it took a superb injury-time save from the Dutchman to keep out Suarez's free-kick.
Pardew was delighted with the resilience shown by his team in front of an appreciative home crowd on a day when several hundred fans had earlier staged a march to protest about owner Mike Ashley's running of the club.
He said: "We showed that, that is in the group, that we can fight when we need to and therefore I am immensely proud of the whole day, really.
"Our fans were brilliant - Steven Gerrard coming to take a corner and being applauded by our fans and stuff like that, it was just a great day for football.
"If Brendan is slightly disappointed, he shouldn't be because he's got a good team and I think we perhaps just deserved the point.
"I enjoyed Paul Dummett's goal because we have had him since he was nine.
"Paul has had to come through some really good class players here to get as close as he has to get that opportunity he got.
"It's great for the academy and great for us that he scored that goal, and his little bunny-hop after was even funnier, so he'll get a bit of teasing about that."
- Sports & Recreation
- Steven Gerrard
- Luis Suarez