Skrtel's performance was one of the highlights of a 5-1 destruction of Arsene Wenger's side on Saturday, with the Slovakian scoring twice in the first 10 minutes to set Liverpool on their way to a first home league win over Arsenal since 2007.
The 29-year-old had been tipped to leave Anfield in the close-season after falling out of favour last term, but has re-established himself in starting XI this campaign.
And manager Rodgers feels the centre-back is one of the division's best in his position.
"It is big credit to him that he's been able to prove me right," Rodgers said. "I brought in a way I wanted to work, on the training field and in games, and for the second half of last season he didn't feature much.
"He had a choice, he could either throw the toys out the pram, or he could sit down with the manager and the coaching staff and see what areas he needed to improve.
"Now, you see a player with great intelligence in his defence, his use of the ball is composed and he has taken on a real leadership role. His performance levels, consistently, have been of a high level.
"He is up there with the top centre-halves in this league, and I am delighted for him."
Liverpool, placed fourth in the Premier League, remain three points clear of Tottenham in the race for the final UEFA Champions League qualification spot.
However, Rodgers is wary of succumbing to a slip-up when his side visit bottom club Fulham on Wednesday.
"Make no mistake, I want to get in the Champions League, both for the club and for the city," the Northern Irishman added.
"But the focus is on improving the players, performance level, and you can see continuation in that development.
"We're still evolving, but I take great pride in seeing development of some of my players.
"We understand that it will be a difficult game (against Fulham). There are no easy games, especially away from home.
"We have a belief and a confidence in our game. Hopefully we can take that into Wednesday."
