The Reds surrendered a two-goal lead to their League One opposition at Anfield on Tuesday evening but ran out 4-2 winners after extra time to progress in the Capital One Cup
The Reds were cruising at half-time in their Capital One Cup encounter at Anfield but saw their two-goal lead wiped out in the second period by the dogged visitors.
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"I think they showed tremendous character, especially going down to 10 men [due to Kolo Toure's injury] and controlling the game at that stage.
"We wanted to win the game and get the goals and they did that. To be 2-0 up and give away the goals we did, we're obviously disappointed, but I can only commend my players for the brilliant character they showed to keep going and you have to give the credit to Notts County."
But the Northern Irishman remains adamant that the extra 30 minutes' play will have little affect on his fit squad members ahead of Sunday's clash with Manchester United at Anfield.
"We've got plenty of recovery time now for the players," Rodgers insisted. "That was the idea, that I could put some of the senior players in knowing there was enough recuperation period after the game and obviously to give our young players some experience tonight.
"They'll all be fine, they'll recover well and we'll be excited now looking forward to that game on Sunday."