Moyes has taken over at West Ham United until the end of the season.
The West Ham co-owner told the Sun newspaper [08/11 printed edition, page 56] that Moyes' appointment was a gamble for the Hammers, adding: "but let's see where we are at the end of the season. I do believe he will keep us up."
Moyes was sworn in on Tuesday as Slaven Bilic's replacement, but the Scottish boss has only signed a six-month deal at the London Stadium.
And discussing the Sun's story on Talksport on Wednesday [08/11, 08:20], Wilkins said: "I think Mr Sullivan has been bang out of order to be perfectly honest - bang out of order."
The former England midfielder went on to state that West Ham's problems are more deep-rooted than any managerial appointment, before adding: "I think Mr Sullivan is barking up the wrong tree, he should have given David at least two and a half years."
Moyes spent the bulk of his managerial career at Everton, where his work was recognised by Sir Alex Ferguson, who oversaw the 54-year-old's appointment at Manchester United upon his retirement in 2013.
But Moyes would last less than a year at Old Trafford, and later left Real Sociedad and Sunderland within the same timeframe.
He finds West Ham 18th in the Premier League, with a difficult run of winter fixtures ahead.
Was Sullivan right to call Moyes' appointment a gamble?