The Spaniard was in the running to take over from the sacked Kenny Dalglish and cut short a family holiday to meet Reds principal owner John Henry in Florida over the summer.
Martinez still maintains he was offered the job and turned it down - Liverpool managing director Ian Ayre insists Rodgers was their first choice - but that is of little consequence to the current incumbent.
"I have a lot of respect for Roberto," said Rodgers.
"He is a guy who has been at the top of the game now for a few years in this country.
"Our philosophies are along the same lines in terms of how we want to work.
"I don't know if he was close to getting it or not but it is a game that is purely about us getting the points.
"Maybe (it is not) for other people but for myself there is no addition to the game other than that we are in a good moment.
"We want to turn draws into wins because we are showing our character and resilience at the moment.
"The players are bleeding the tank dry every week for me, pushing everything into the game, and I just hope we can get the rewards for that and get the wins."
Rodgers took heart from the point his side earned in a 1-1 draw at Chelsea in their last outing.
He said: "We have shown great resilience to come back like we did last weekend without playing particularly well but it is important we win games, especially at home."
Liverpool's home record, and not just under Rodgers, is an issue in itself.
Just three Barclays Premier League victories have been registered at Anfield in 2012, with just one of those coming this season.
Only six points have been accrued from a possible 18 at home - on the road they have a similar total from five games - and Rodgers knows it is a record which has to change.
"The point is no good at Stamford Bridge if we don't win (at home)," he added.
"The players are giving everything in the games, they are pressing and working very well and they just need a bit of luck and that touch of confidence.
"Once we get that, we will go on and improve.
"We just need to win games, which is important if you want to climb the league and that is what we want to do.
"We have to be looking to take maximum points from our home games."
Only one point separates the 13th-placed Reds from tomorrow's [Saturday] opponents, who are unbeaten in their last five against Liverpool including a 2-1 victory at Anfield back in March.
The Latics experienced an upturn in their results, which ultimately saved them from relegation, after Martinez switched to a 3-4-3 formation to make his side more attacking.
"Obviously last year I experienced playing against it (the system)," said Rodgers.
"They have beaten Tottenham and Southampton away this season and it's going to be tough: we've got evidence of that from last year when they came to Anfield and won.
"I know Franco di Santo well as I worked with him when he came to Chelsea from Chile. He has improved each year.
"Arouna Kone is direct and fast and in those transition moments, if there is a direct pass, he can obviously affect it with his pace.
"It is up to us to control that side of the game - but our focus will be on our own performance."
Coincidentally Rodgers has also had cause to tinker with his formation in the last few weeks, also employing a back three on occasions.
"It is a great credit to the players in terms of their flexibility," said the Northern Irishman.
"We've used it a couple of times this season and at certain points and moments tactically it is something the players can flip to.
"In the first half last week (playing 3-5-2) defensively we were solid enough but I felt it maybe had an impact on our pressing, which we like to do from the front and it is easier to do that with three players.
"It worked reasonably well for us but didn't give us the attacking impetus we wanted but it is something to look at in the future.
"It is something we can always look at. I'll always look at tactics to win games."