A run of seven consecutive Premier League wins saw the Toffees climb above Tottenham and then Arsenal into fourth spot and in sight of a first top four finish since 2004-05 in their manager's first season in charge.
|5/4||Everton are 5/4 with Paddy Power to finish in the top four this season|
"It was a hell of a challenge," Martinez is quoted as saying by the Daily Mail.
"But it has always been my vision that Everton would fight for Champions League football - because of the history, the heritage and everything we have as a club we should be challenging for Champions League.
"It was the week we beat United and played so well at Arsenal that the chairman said, 'maybe I can see what you were saying'.
"The [current] points tally is the biggest one [Everton have had] in the Premier League. So if the leaders [in the squad] hadn’t accepted we would go in that direction, it would never have got the group together.
"So huge credit goes to the senior players in being brave and saying they will try this."
Arsenal moved back into fourth place with a come-from-behind win over West Ham on Tuesday, but three points against Crystal Palace on Wednesday will see Everton again leapfrog the Gunners.
And Martinez feels under no pressure to finish fourth, insisting counterpart Arsene Wenger has, unlike him and his squad, "something to lose" if his team miss out on Champions League this season.
"There is no pressure on us," he said. "We have nothing to lose. I think the pressure comes when you have something to lose. We are in a position where we have everything to gain."