The Toffees can make up ground in the race for a top-four spot on Sunday when they visit White Hart Lane against a Spurs side facing injury worries after Europa League action
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Spurs lost Gareth Bale, William Gallas and Aaron Lennon to injury against the Swiss side, although Everton will be without Steven Pienaar and Marouane Fellaini through suspension.
Stuart told talkSPORT: "It's going to have to be a big afternoon for the Toffees because Tottenham are in some decent form.
"They've got a tough game of their own against Basel so hopefully they will be struggling a little bit leg-wise on Sunday and Everton can take advantage.
"Irrespective of what happens, Everton have had another terrific season."