Brendan Rodgers never identified names or positions when accusing Liverpool of lacking leaders last season but the demotion of Martin Skrtel from central defence suggested one candidate. The Slovakia international considered leaving Anfield as a consequence but chose instead to confront his manager's criticism. There are no question marks over his authority now.

Two early goals from a centre-half in the 5-1 rout of Arsenal on Saturday naturally drew attention to Skrtel but it was his latest composed, unruffled defensive performance that increased the satisfaction for Rodgers. Skrtel has been the most consistent performer in a Liverpool defence that has endured frequent disruption this season, although it is a campaign he almost did not stick around to see.

The 29-year-old was a peripheral figure in the second half of Rodgers' first season at Liverpool, losing his place to Jamie Carragher and struggling for an opportunity to make amends for the dismal FA Cup exit at League One Oldham Athletic. Liverpool's desire for new central defenders was no secret throughout last summer and ultimately three were acquired – Kolo Touré, Mamadou Sakho and Tiago Ilori – and Skrtel found himself behind the Ivory Coast international Touré as well as Daniel Agger when this campaign began. The Napoli coach, Rafael Benítez, the man who brought the defender to Liverpool from Zenit St Petersburg in January 2008, was among those who sensed an opportunity to prise Skrtel away from Anfield.

"I wouldn't be lying if I said that after last season I was thinking about leaving Liverpool," Skrtel said. "But it is not an easy decision to leave a club like this. I have been here for six years and Liverpool is, for me, one of the biggest in the world. I decided to stay and fight for my place. After games like Arsenal I am just happy I did and proud to be here. There was a lot of talk and rumours that I would go but I was happy to stay. Arsenal was one of those games why you play football. It was a great atmosphere, just a perfect performance and a perfect day."

Rodgers may have harboured doubts over the Slovakian in August but before Wednesday's visit to Fulham he heralded Skrtel as one of the best central defenders in the Premier League. Liverpool, added the manager, have also gained another leader.

The Liverpool manager said; "He looks a class act. It's a big credit to him that he's been able to prove me right. Obviously I want a certain way on the training field and in games and he didn't feature so much in the second half of last season. A player has the chance to either kick up a fuss or sit down with his manager and see what areas he can improve. All credit to Martin; he has taken the responsibility to be a better player. His use of the ball is more composed, he's taken on a real leadership role with the young players and his consistency has been at a really high level.

"He is up there with the top centre-halves in the league. I'm really pleased for Martin. He's a good man and has shown that even an international player can learn if he is willing to. But I wouldn't have let him take a penalty for his hat-trick on Saturday if we had got one."

The issue of leadership, of taking responsibility in defence and adding a voice on and off the pitch has clearly been embraced by Skrtel this season. "I am trying to become a leader here," he said when asked what has changed. "After the second half of last season when I was on the bench, it wasn't easy for me. Before the season I wanted to start the games and show people I could play. I just try and work hard every day in training and when I get a chance try do my best and help the team. It was great to get one goal on Saturday, never mind two, and I am just happy to help the team and get the three points. I have never scored more than one goal in a game before. It was something special. I wasn't thinking about a hat-trick. To get two – I am very happy for that."

Arsenal were the seventh team this season to concede four or more goals at Anfield but Liverpool have not always found the same ruthlessness away from home. Skrtel said: "We have showed some perfect performances at Anfield and we must try and do it away as well. Fulham is going to be a tough game because they are fighting against relegation but we just need to go there and play with the same intensity that we did against Arsenal."