He named captain Steven Gerrard on the bench along with Mario Balotelli, Raheem Sterling, Jordan Henderson and Coutinho - all players who would have expected to have been in a full-strength side.
The move was heavily criticised on Twitter, with it appearing like an admission that Liverpool had little chance at the Bernabeu even with their best players available.
The Reds have made a terrible start to their first European campaign for five years, losing meekly to Real Madrid at Anfield, going down to Basel and scraping a win in their opening game against Ludogorets.
Among those who think so is the wife of Liverpool defender Dejan Lovren who posted a picture of their daughter along with the message: "Why my daddy doesn't play???"
On Twitter, former England striker Gary Lineker wrote: "Rodgers has left out Henderson, Sterling, Balotelli, Gerrard and Coutinho at Real Madrid. He has, though, thrown in a white towel.
"Selecting a weakened side in Europe's premier competition, especially against Real Madrid, is unbefitting of a club of Liverpool's stature.
"If I were one of Liverpool's star players, I'd be choked to be left out of a game at the Bernabeu against the European Champions."
Scholes, working at the match as an ITV pundit, said Gerrard would have no trouble playing in Europe on Tuesday and in the Premier League against Chelsea on Saturday.
The former Manchester United midfielder said: "I think Steven Gerrard is capable of playing in this game and on Saturday. He can still have his two-day rest.
"I think that's why he gave up international football, to play in games like this. I don't think he'll be happy tonight."
Predictably, Twitter went into overdrive. We've picked out some of the best...
Brendan Rodgers right now... pic.twitter.com/s8NQ6s0dlb— TheSPORTbible (@TSBible) November 4, 2014
Liverpool's team news makes its way Real Madrid's dressing room: http://t.co/se2svNAttg— Paddy Power (@paddypower) November 4, 2014
Rodgers resting all Liverpool's big guns for tonight's game in Madrid... pic.twitter.com/wEgDSaNgrZ— Paddy Power (@paddypower) November 4, 2014
Can't believe Brendan Rodgers has fielded the same team as the one from the Father Ted episode Escape From Victory. pic.twitter.com/BbUkL00TFy— Chris Parkes (@rocknrollparksy) November 4, 2014
Brendan Rodgers... pic.twitter.com/kBLXVODiqR— Pro-Direct Soccer (@ProD_Soccer) November 4, 2014
Brenda Rodgers! pic.twitter.com/6Tpzptf0VA— Mark (@1878Mark) November 4, 2014
When Kolo entered the dressing room and was told he'd be facing Ronaldo https://t.co/kfkMrqyuGc— Bae (@Mike_Nkansah) November 4, 2014
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