The defender struck twice in victory over Arsenal.
"I would be lying if I said I didn't think about leaving," Skrtel told the Liverpool Echo.
"It wasn't easy for me after last season. I was on the bench in the second part of the season and that was something new for me.
"But it is not easy to leave a club like Liverpool because they are still one of the best clubs in the world. After six years here it was not easy to say 'okay, I'm leaving'.
"Before this season started I just said to myself 'I will fight and work very hard to try to show people I am able to play and start the games'.
"I tried to work very hard in training every day and when I got a chance to play I tried to do my best to help the team.
"After games like Saturday's I am just so glad and so happy that I stayed."
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