Redknapp was left fuming by what he called two "scandalous" decisions after QPR's 2-1 defeat to West Brom on Boxing Day.
Referee Chris Foy allowed a controversial own goal by QPR keeper Robert Green to stand and waved away appeals for a penalty when Albion defender Liam Ridgewell appeared to handle the ball.
Redknapp said: "We see penalties given when the ball is kicked from a yard away and Ridgewell's got his hands up.
"I asked the linesman how did he not see the penalty. Ridgewell's hand was up there, it's the most blatant handball and he couldn't see it.
"The linesman said it was murky down in that corner and he couldn't see it, so maybe he should go to an opticians...it's just poor refereeing. I had him [referee Foy) at Stoke last year when I was Tottenham manager and he let three penalties go, so what's the point in talking to him?
"We have had two terrible decisions that have cost us dearly."
Mancini criticised the performance of referee Kevin Friend following Manchester City's 1-0 defeat to Sunderland.
"The referee ate too much for Christmas. He was not in good form," said Mancini.
"He and the linesman, I think, after Christmas, it can happen to have a bad performance like today."