Everton entertain Arsenal on Sunday in what could prove to be the defining match in the race for a top-four finish in the Premier League.
Arsenal are currently in the driving seat for the final Champions League qualification spot, although a run of five consecutive wins has seen Everton move to within four points of their visitors with a game in hand.
The sides have already met twice at the Emirates Stadium this season, drawing 1-1 in the league in December before Arsenal ran out 4-1 winners in the FA Cup quarter-final last month.
And Martinez, who is without captain Phil Jagielka (hamstring) and Steven Pienaar (knee), believes his side will have added motivation for the crucial clash following their Cup exit.
"The game we played in the quarter-final of the FA Cup left us with a sour taste," said the Spaniard. "And we need to make sure we use Sunday's game to perform as well as we can.
"It (the result) could have a huge bearing (on who finishes fourth).
"We are fighting with a direct rival that we admire and respect, and are in this position every season - they find a way to perform in these big games."
However, Arsenal boss Arsene Wenger disagrees with his counterpart and remains calm ahead of the match.
Arsenal have not lost at Everton since March 2007, but the Frenchman insists the result at Goodison Park will not definitively decide fourth place.
"It's an opportunity to go forward and as well an opportunity to make a distance with Everton," Wenger said.
"Everton are a good side, that's why they are where they are.
"For us it's very difficult to imagine the impact it will have on finishing fourth, but it's a game we want to win."
Aaron Ramsey has provided the visitors with a boost as he is in line for his first appearance since suffering a thigh injury at West Ham on Boxing Day, and Nacho Monreal (ankle) is also available.
However, Kieran Gibbs (ankle) and Serge Gnabry (knee) are doubtful, while Jack Wilshere (foot) and Mesut Ozil (hamstring) are definitely out.
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