The Toffees battled to a point against Stoke City, with Potters striker Kenwyne Jones cancelling out Ryan Shawcross’ 36th-minute own goal.
It kept Moyes’ men in the hunt for a Champions League spot, with fourth-placed Tottenham Hotspur two points clear of the Merseyside outfit.
Stubbs, who was part of the Everton side that qualified for Europe’s premier club competition in 2005, believes the current crop at Goodison Park are good enough to pip Spurs if they can piece a run together.
“I was very impressed with Tottenham when they played us last weekend, even though we won the game, they’ve got a fantastic squad and if they put a run together they would be serious challengers for fourth place,” Stubbs told talkSPORT.
“They’re one of the better teams I’ve seen this year. But you never know, with Tottenham you do get that up and down rollercoaster of results.
“Everton have just got to be in there. If we’re in there pitching then, with our spirit and our comradery amongst the players and the fact we’ve got a great manager, I think we’ve got a chance [of finishing fourth].”
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