Liverpool were handed a two-goal lead at Anfield when Wes Morgan and Danny Simpson were both punished for handballs inside the penalty area in the first half – Steven Gerrard converting both spot kicks.
However, they were unable to hold onto the victory as Leicester showed their battling qualities for a second-successive away match.
Having withstood heavy pressure to beat Hull City 1-0 on Sunday, they defied the odds again as David Nugent and Jeffrey Schlupp earned a unexpected point.
Rodgers admitted his side had not done enough to deserve all three points, and rued too many mistakes in Liverpool's play.
"I thought we got what we deserved in the end," he said. "I didn't think we played well in all honesty, and I thought Leicester played very well.
"We found ourselves two-nil up in a game we didn't deserve to be, we still created chances but it was always a dangerous game.
"Leicester played very well, they've got players at the top of the field with speed and that's always very dangerous.
"We're obviously disappointed at being two-nil up and conceding the goals we did.
"Overall there is a little bit of frustration, but I can't be too unhappy because I didn't think we played well enough to merit a win to be honest."
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