The Merseyside club are one point behind Arsenal who occupy fourth spot, although the Gunners have a game in hand which they play on Monday night against Newcastle.
Everton lost to Southampton yesterday thanks to two own goals, which infuriated Martinez, and now the Toffees face tough games against Manchester City and Hull away to finish the season.
Despite Arsenal now having pole position, Martinez has not given up on a top four finish.
“It’s clear that you want to get as many points as you can. For us it hasn’t changed,” Martinez said.
“It’s the same for us after beating Manchester United last week. It didn’t mean we were going to get into the top four and now it’s exactly the same.
“Eight wins or 24 points out of 30 is a phenomenal run and we’re going to give everything we’ve got for the next six [points].
“That’s the only focus we’ve got – how many points we can get by the 11th of May. Then we’ll look at the table and see where that’s got us.”
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