Leon Osman has backed the Blues to sign off their season at Goodison Park with three points.
After Sunday's 0-0 draw at Liverpool, Everton now have just two Premier League fixtures remaining.
The first of those, and the last of the 2012/13 campaign to be played at Goodison, comes this Sunday against West Ham (3pm kick-off).
And with the Blues still mathematically capable of finishing in a European place, midfielder Osman says victory against the Hammers is paramount.
He told evertontv: "We've got to keep going and try to win our last two games and hope that's enough."
Fifth-placed Tottenham are the only team that the Toffees can still catch - and they head to Stamford Bridge for a crucial clash with Chelsea.
Anything greater than a point for Andre Villas-Boas' men will put Everton out of the European equation, but the Blues' belief has not diminished.
Osman continued: "It's going to take a disaster from one of the teams above us for us to get in there, but we can only hope that [the draw at Anfield] is a good point."
Pivotal to Sunday's derby draw was the efforts of Everton's next permanent captain Phil Jagielka.
While centre-back partner Sylvain Distin saw a goal controversially disallowed, the England man led by example at the back to silence Liverpool's attack.
"He was terrific," noted Osman.
"He made some fantastic blocks, especially in the first half.
"He defended really well and we defended really well as a team."
Tickets for the final home game of the 2012/13 season are now on sale.
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