Aaron Lennon’s winner lifted Everton to 13th – nine points clear of the relegation zone – with the club securing consecutive Premier League wins for the first time since October.
“Certain games sometimes call for certain styles of play, and the way the game goes dictates how you end up playing,” said Osman, who played the full match as Everton claimed a fourth away league win of the season.
“Every time we lost the ball it was sent up to the edge of our box, so we had to fight and scrap for second balls.
“It was a scrappy match defensively but we proved we can do that side of the game and then, once you’ve done that, you have the opportunity to hit teams on the counter-attack, which we tried to do.
“There was probably not as much football played as we usually like but there’s no problem winning like that as well.”
Martinez’s team went out of the Europa League on Thursday following a 6-4 aggregate defeat to Dynamo Kiev, so Osman appreciates the importance of the victory at Loftus Road.
“It was a massive win for us after we suffered a big disappointment in the week,” said Osman. “It hasn’t quite happened in the league this season so to put back-to-back wins together was really important for us.
“We were terrific at the back, especially Phil Jagielka. I thought he was at his best and we dealt with all their situations quite well. “It was always going to be difficult with the pitch as it is and with the way they played.
“They made it difficult for us but we stood up to that challenge head on and came away with a victory. We’ve still got eight games left and we’re going to concentrate on those games now and just see how many points we can pick up.”
Everton next face Southampton at Goodison Park on April 4.