With five minutes of normal time remaining, the Spain international managed to let a David Templeton shot squirm though his grasp and over the line before Luis Suarez saved his blushes scoring the winner three minutes later.
Rodgers told reporters: "Pepe has been brilliant since I’ve been here. He’s been a pivotal part of how we work. He’s been excellent off the field, a real good guy who understands the ideology of what we’re trying to do.
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"Unfortunately for goalkeepers it’s part and parcel of the game. There’s no blame attached – unfortunately for goalkeepers they make a mistake and sometimes it leads to a goal.
“An outfield player makes a mistake and they’ve got their mates to recover. It will happen sometimes but we move on."
The former Swansea boss also hailed his side's work ethic and praised Suarez for his late clincher, although bemoaned a plethora of wasted opportunities earlier in the game.
Rodgers said: “One of the key things that I’ve noticed in the group is that they have hard work and integrity, I think the players have been absolutely magnificent since I’ve come in.
“They’ve given me everything and as each day goes on we’re getting closer as a group. That spirit really took us through Sunday’s game and took us through tonight’s game so it’s very important that when we went 1-0 behind we didn’t get disappointed.
“We came back and Luis’ most difficult chance he took, a wonderful run and finish. We probably could’ve put the game to bed earlier.”
Adam Morgan made his first start for the Reds in the match, and Rodgers revealed he will be looking to give more young players a chance in the team while he is in charge.
He added to ESPN:: "He’s a local boy, from Liverpool, and it’s important for me to give local boys who came through the ranks a chance.
"It was important for him to get his first start, and it’s important for me to give local boys a chance, and it’s something I’ll look to do."