Kompany was a doubt for the match at Anfield, but the 28-year-old still managed to play for his side, although he made three errors that led to Liverpool's three goals.
Redknapp wrote in the Daily Mail: "After his performances this season plenty of people were ready to say Vincent Kompany was the best defender in the world, but Sunday was a game to forget.
"He played a part in all three Liverpool goals, with Raheem Sterling's sidestep catching him out so badly he had to pay to get back in. Then he was easily brushed off by Martin Skrtel for the second and made a hash of his clearance for the third.
"The Belgian had one of those days that we all have in football and he will want to move on, but for City it came at a big price."
City now trail Liverpool by seven points in the race for the Premier League title.