Latics opened their Premier League campaign in August with a 4-0 home defeat against newly-promoted Blackpool and were hammered 6-0 by Chelsea at the same venue in the following game.
It appeared as if Martinez's preference for attacking play was leaving his side horribly exposed, but a 1-0 win at Tottenham halted the slump and Wigan have now taken nine points from their last six league games.
Coyle, whose team travel to the DW Stadium tomorrow, is also an advocate of flowing football and has hailed the Spaniard for persevering with what he believes in.
"I have known Roberto for many years and he is very much a purist," Coyle said.
"He loves passing and moving the ball, and there are tremendous players in offensive positions for Wigan - the Rodallegas, the N'Zogbias. Di Santo is a terrific player, Boselli was a big-money signing.
"These are very good players and they look to retain that possession and pass and move the ball.
"All credit to Roberto because he came in for a bit of flak, as we all do as managers, at the start of the season and they have seen their way through that.
"He has shown tremendous mental strength and tremendous belief in what they are doing at Wigan and they have started moving themselves up the table.
"We know we are playing against a very good side and we are going to have to be at the top of our game to try and achieve a positive result and get points.
"But the way we are going about it, I believe we can be positive and try and impose ourselves on the match."
Bolton have adopted a more attractive style themselves under Coyle which has served them well this term.
Currently sat in seventh place and with two of their players in the last England squad, the club looks to be in rude health.
Midfielder Fabrice Muamba has been tipped in some quarters to join his club mates Gary Cahill and Kevin Davies in the senior national set-up and Coyle hopes seeing Arsenal's Jack Wilshere - who was on loan at the Reebok Stadium last season - make the jump from the under-21s to the full squad will encourage Muamba he can do the same.
"Being an English club, you want your players representing the country," Coyle said.
"Fabrice has done ever so well in the under-21s and he has to continue that progression.
"I think the great thing with the under-21s is that they will look at the squad and see that Jack has really burst from that squad into the full one.
"I would hope they will all look at that and think 'I can be the next one'.
"But the only way to do that is by performing consistently in the Premier League and showing Fabio Capello 'look, I'm a young talent and I'm ready to play for you."