The Premier League strugglers confirmed the appointment of Dyche on a two-and-a-half-year contract on Monday, with two other names in the form of Ian Woan and Steve Stone also joining the club in his backroom team.
The road ahead is not going to be an easy one for the former Burnley manager, whose side are currently in the relegation zone, two points off safety.
Stubbs, while wishing Dyche and his backroom staff well on their appointment, urged patience on behalf of the fans and the board as he feels that a final judgment will only be possible once Everton complete their quota of 18 matches between now and the end of the season.
“Good luck to Sean Dyche and all his backroom staff”, Stubbs wrote on Twitter.
“We will be right behind him, he needs to lift these players but he also needs new additions to help this squad!
“Let him be judged as a Everton manager from now and 18 cup finals begin Saturday.”
Everton did not manage to add to Dyche’s squad on transfer deadline day, failing with a number of bids for targets.