Martinez, now manager of Everton, steered the Latics to FA Cup glory following a shock win over Roberto Mancini's City in last season's final.
Goals from Jordi Gomez and James Perch on Sunday ensured lightning struck twice in this year's quarter-final at the Etihad Stadium.
Despite both clubs having different managers at the helm this time around, Rosler was astute enough to take a leaf out of his predecessor's book in a 2-1 victory which ruined City's chances of a historic quadruple.
Gomez and Perch scored in either half to continue Wigan's love-affair with this competition and although Samir Nasri reduced the deficit, Wigan's defence stood firm to secure a semi-final showdown with Arsenal at Wembley.
"I started with Roberto's tactic from last season," said Rosler, whose side join Bayern Munich, Chelsea and Barcelona as the only teams to have beaten City at home this season.
"He won the FA Cup by putting out a very brave game-plan and also I saw the league game here (against Wigan last April) where Manchester City won in the last five minutes 1-0 and Roberto's team played periods to perfection.
"I tried to replicate parts of it but bringing our own intensity in terms of our pressing, our counter-attacking and the willingness to attack with wing-backs at the far post - like the second goal.
"I felt first half we surprised Manchester City because a lot of teams show Manchester City, deservedly, a lot of respect. I felt if we sat back and just tried to defend and just hoping for the best we would have no chance."
The hosts, seven days on from their Capital One Cup final triumph, were lacklustre in the first period.
But sparked by Nasri's goal and the introductions of David Silva, James Milner and Edin Dzeko from the bench, they flooded forward in the closing stages of an enthralling cup clash.
They almost grabbed an equaliser too but Wigan captain Emmerson Boyce somehow diverted Dzeko's simple tap-in over the bar with a piece of heroic defending.
"I just saw the block - unbelievable," said Rosler. "I'm a big believer that you need match-winners at both ends, not only in the attacking box, but in your own box. That tackle was a match-winning, decisive moment for us.
"Both tackles, the one Perchy had when he scored, and the one Emmerson Boyce had when he denied Dzeko the goal, that has shown the desire and the will-power we have shown today. I can only take my hat off to the players.
"Emmerson is a symbol of that, not only today but since I've worked in the club."