The England left-back signed a new four-year deal last week to end speculation about him moving to Manchester United to be reunited with former Everton boss David Moyes, who had failed with a summer move for the 29-year-old.
Ironically Moyes' departure brought Martinez to the club from Wigan and his new approach helped make up Baines' mind.
"It was great to sign and commit to the club and put everything else to bed and be able to focus on football and the future - my future and the club's future," Baines told evertontv.
"It has been really positive for the most part this season and I've been really impressed with the manager's approach to everything.
"The various aspects to what he does and the way we approach games is asking new questions of all of us, whether you've been here a few months or a few years.
"It is challenging and has freshened the place up. It was a fresh start for all of us and it was exciting because it was such a change and that was a big part of it."
Martinez has implemented a passing philosophy and encouraged his players to enjoy more freedom and have more possession of the ball.
That more liberated approach contrasts with Moyes' more pragmatic tactics and it has brought out the best in the players.
Everton currently sit fifth, just two points behind city neighbours Liverpool, and still in with a real chance of Champions League qualification.
Baines believes the return of European football, coupled with ending a trophyless run stretching back to 1995, have to be the club's two main aims and he believes Martinez's approach make success in both a reality.
"When you change manager and the previous manager has done a really good job there are going to be question marks but he's answered a lot of questions already," said the defender of Martinez, who against the odds won the FA Cup with Wigan last season.
Everton face a fifth-round tie against another of Martinez's former clubs, Swansea, next weekend.
"People might have viewed this season as transitional and we may have got away with it if it hadn't gone great," Baines said. "But the fact is the lads have done really well, applying those different aspects of the game, and we've got some really good performances and results.
"It is the same game just a slightly new method and he is trying to make us well-drilled in it.
"It is still a work in progress because every time we get comfortable with certain aspects he'll start to introduce something else, which is sensible because if you come in and throw everything into the one pan and try to get it all going at the same time it maybe doesn't work out.
"He is introducing things and we are slowly improving as a team.
"The manager wants us to have that confidence on the pitch, a bit more arrogance on the ball, and that is something he is trying to instil into the players and that comes with performances and results.
"We would like to improve again and give ourselves the best chance of getting back into European football.
"There is no limit if you can do it well; it is a style all the top teams in Europe play so we have to up our level as players to try to execute it.
"If we managed to qualify for Europe then the style we play immediately translates to fitting in with European football, we don't need to adapt.
"Getting back into Europe is a major goal. The cup competitions have always been important to us but it would be huge to bring that sort of success back to the club.
"For a club as well supported as Everton to be starved of that success makes everyone hungry and everyone is chomping at the bit to work towards that."