Baines' side are set to face old boss David Moyes at Goodison Park for the first time since the long-serving Toffees manager moved to Manchester United last year.
Martinez, formerly of Swansea City and Wigan, has guided Everton within touching distance of a UEFA Champions League play-off spot, as they trail fourth-placed Arsenal by one point.
Meanwhile, Moyes' United are set for their worst finish since they were 13th in 1989-90, and their first non top-three placing since they were sixth in 1990-91.
Baines said Martinez has been stringent in enforcing his game plan throughout the season.
"That's been the big thing for me, the difference in the style of play, committing to that and not feeling like we have to adapt to the opposition," Baines said, as quoted by the Liverpool Echo.
"The new manager has that confidence and belief in himself, in his own blueprint. And then in us. He tells us we're not going to change, we're just going to improve constantly and keep practising until we get to the level where we want to be.
"Stick to it, don't compromise, get better at it.
"He also spoke about the Champions League from the start. He didn't shy away from it. He came in and straight away, he set the bar high.
"We might have got away with a fairly ordinary season, the changeover with the new manager, the first season, a transitional season.
"But he didn't want to accept that. He wanted to improve on what we'd done before, and we've done that."
Baines said Martinez deploys a high defensive line that drives their positive agenda, with the club scoring 55 goals in 34 league appearances, and having a better goal difference than powerhouses Arsenal and Manchester United.
"It's very different. The full-backs at Everton are more advanced now. If Tim Howard has the ball, I'll be encouraged to be higher up the pitch and that creates more space for the midfielders. We can then start our play, building up from the back," Baines said.
"People will say there's a risk involved, and there are times, as a defender, when I'm one side, Seamus is on the other, and I'm thinking: 'I could do with being 15 to 20 yards further back here.'
"But the idea is we stick to it, keep the ball and build.
"What the manager says is: 'We're going to get so good at what we do, we're not going to compromise that, we're going to stick to our principles and just get better because the top sides, the really top teams who have mastered this way, are the ones that gets success.'"
Everton and Manchester United kick off in the late game on Sunday, after top-four rivals Arsenal are away at Hull City earlier.
