Martinez was in charge at Swansea until June 2009, with Rodgers joining the club in 2010, seven months after he was sacked as Reading manager.
Paulo Sousa had a year-long spell at the Liberty Stadium prior to Rodgers' arrival but the positive influence of Martinez was still in evidence.
The current Liverpool boss feels the Spaniard's progress was crucial in helping him adjust at Swansea, where he guided them to the Premier League prior to being lured to Anfield.
"He did a terrific job at Swansea for the couple of years he was there, it made my job easier going in," said Rodgers.
"I could then work on other aspects. Every manager who comes in after someone, you will always respect what he has done.
"Certainly with me and Roberto, he did an excellent job there. I was there to move it on and hopefully move the club forward again."
Rodgers is convinced that ethos is evident in the way the two managers go about their work, despite some differences in their style of play.
"There are principles that are the same. We both like to have teams that can control and dominate the game with the ball," he added.
"I always want to play offensive and attacking football but always with a tactical discipline.
"I like to play high intensity attacking football but our defensive record this season has been good, the second most clean sheets in the league.
"Ultimately it is about winning and Roberto and I, whatever style or methods we play, you have to get results and that is what you will be judged on."
Liverpool have not won at Wigan since September 2007 and the Latics claimed victory in seven of their final nine matches last season, sparked by a 2-1 success at Anfield, to preserve their Premier League status.
"They did brilliantly last year with the run they went on. It was a huge mountain they had to climb to stay in the league and they did it," added Rodgers.
"Traditionally it has been difficult for them. Dave Whelan (Wigan's owner) and Roberto have built it up well and tried to build a team that can stay in the Premier League.
"They will be looking to sustain it and they seem to come up with the answers every year.
"We will give the opponent respect and do our work and look to bring our game into it."