The Slovakian centre-back attempted a blind backpass to Pepe Reina - giving Tevez a free run at the goalkeeper, whom he rounded to level the scores, but Rodgers refused to put any blame on the defender who gave his side the lead with a thumping first-half header.
|18/1||Liverpool are 18/1 with William Hill to beat Arsenal 3-0 next Sunday
"There's no blame to Martin Skrtel, I'd rather have players wanting to get on the ball," Rodgers told Sky Sports. "The courage he has to get on the football and try to play is what is the most important thing."
The game also saw home debuts in the Premier League for Raheem Sterling and Joe Allen, and Rodgers was pleased with both players, who put in "phenomenal" performances, according to the Anfield boss.
He added: "It was a brilliant performance I thought. There were a lot of questions asked of the team coming into such a big game but I thought the players were incredible and sometimes the best team doesn't win, and I think we were the better team.
"From what I've seen today, last week was a one-off and today I thought they were terrific.
"The plan was going perfect but then I thought tactically the ability to press at the right time and to drop off and to block was very good. I'm very, very proud of the team."
Loan signing Nuri Sahin was in attendance, but was unavailable for the game and forced to watch from the stands and Rodgers says he is planning on bringing in more players to add depth to the squad.
He continued: "I just think the players need some help. Obviously we lost a lot of players in the summer and we've only replaced what went out and not even that.
"The squad is a bit shallow, there's absolutely no doubt about that but we need to get a few in just to help the players that are here."