Former England striker Lineker was among those to express amazement at the line-up chosen by Rodgers for Tuesday's meeting with the European champions in Group B of the UEFA Champions League.
Captain Steven Gerrard, Raheem Sterling and Jordan Henderson were among those to be left on the bench as Rodgers made seven changes to the team beaten 1-0 by Newcastle United on Saturday, seemingly with one eye on this weekend's clash against Premier League leaders Chelsea.
In a series of posts on Twitter, Lineker suggested Rodgers had "thrown in a white towel" and said: "Selecting a weakened side in Europe's premier competition, especially against Real Madrid, is unbefitting of a club of Liverpool's stature".
Yet after seeing his side go down by just a solitary Karim Benzema goal, two weeks after Real had eased to a 3-0 triumph at Anfield, Rodgers remained defiant over his decision-making.
"Gary is a figure I respect and he was a top player but he has never been a manager, so probably doesn't truly understand what you are up against in terms of planning forward that way," said the Northern Irishman.
"We were certainly far from throwing it away. You know, Cristiano Ronaldo has scored in every game since the Spanish Super Cup final [and didn't score in this match]. That shows you how hard we defended and how hard we worked.
"Right to the very end I think my players put in a performance that showed their passion, their commitment and their quality. That would be my answer. I am not bothered about the criticism."
Lineker did post a further tweet after the match, adding: "Rodgers intimating that many of his players were dropped for being awful at Newcastle rather than being rested. If that's true, fair enough."
While Real are now assured of a place in the last 16, Liverpool trail second-placed Basel by three points in Group B with two matches to play.
