Aaron Lennon's 77th-minute winner moves Everton nine points clear of the relegation zone after Rangers' Eduardo Vargas had earlier cancelled out Seamus Coleman's first-half strike.
Martinez's side climb to 13th in the table, having bounced back from a disappointing 5-2 Europa League defeat to Dynamo Kiev on Thursday.
"It's probably the most satisfying win I've had since I arrived at Everton," Martinez said.
"The amount of emotion we shared on Thursday and we got back very late - we've found it very difficult this season after Europe.
"We are adapting towards being a team that can cope with being in Europe.
"Coping with the goal threat that QPR are going to throw at you takes a lot of character and guts
It wasn't a day for a technical performance on the ball, i t was about being a strong group and showing we have a strong will
"It was a very important three points today so the satisfaction was immense."
Lennon's decisive strike 13 minutes from time was his first goal for Everton since joining the club on loan from Tottenham in January.
Martinez was reluctant to discuss the possibility of making Lennon's stay permanent but admits he has been delighted with the winger's contribution.
"It's too early to say at the moment (whether we will sign him permanently)," Martinez said.
"Since he's arrived he's wanted to contribute and be a big part of the team.
"His performance against Newcastle was his best performance since he arrived.
"He came to Kiev, he shared the emotions we all had and that showed today.
"He had a real will
He wanted to show he had fresh legs and I thought that was his best performance by far for Everton, not just in scoring the goal but in the manner he worked for the team.
"He looks like someone who has been with the group for a long, long time."
The defeat is QPR's fifth in a row since Chris Ramsey was confirmed as manager and means Rangers remain on 22 points, four points adrift of safety ahead of crunch visits to fellow strugglers West Brom and Aston Villa.
After those two games, Rangers face Chelsea, West Ham, Liverpool and Manchester City before finishing the season at home to Newcastle and away to Leicester.
"I don't think we need a miracle but we do need a miraculous run of form to get us out of this," Ramsey said.
"But I think we're capable of doing that
How many points do we need? I think four wins out of eight will probably keep us up this season
I think it'll be a low total."
Ramsey added: "We need six points against West Brom and Villa.
"There's no point in saying, 'we're going to go there and try to get a point', we need to win games and pretty quickly."
Source : PA
Source: PA