Redknapp wrote in The Sun: "Taking over from Alex Ferguson gets you about five minutes to settle in before the expectation starts piling up.
"He will be expected to win a first trophy in his debut year in charge of this country's biggest club. Success will be classified as winning the Premier League and/or the Champions League.
"Moyes has got it a lot tougher to improve on this United team than Fergie did when he took over with them in the doldrums in 1986.
"As champions it is difficult to go up from there."