Darel Russell's 68th-minute winner gave City a massive boost in their battle to stay in the Championship, while putting another dent in the Londoners' bid to reach the play-offs.
Rangers are without a victory in six games and have not won at home since December.
Their season is in danger of petering out despite the high expectations of the club's Flavio Briatore-led board, but Sousa insisted: "I am very enthusiastic about my team and I'm proud of them.
"We played great football and created a lot of opportunities.
"Norwich made one shot and one goal. Sometimes football is like that and you don't get what you deserve.
"I have told my players I am not only proud of them when we win, but also when we lose, and I am proud of them tonight.
"My team played very well. We lost, but we must have our heads held high. We did some great things."
And Sousa refused to give up hope a top-six finish, saying: "When you have a mathematical chance, you need to think of the play-offs.
"When you're closer to them it's better, but while we still have a chance we must believe."
Russell, playing in place of the axed Mark Fotheringham, profited from a defensive lapse and a mistake by keeper Radek Cerny.
After Lee Croft robbed R's defender Kaspars Gorkss, Wes Hoolahan pounced on the loose ball and found Russell, whose shot slipped through Cerny's hands and into the net.
Russell's goal - his fourth of the season - soothed Norwich's anger at being denied a first-half penalty after Croft had gone down in the area under a challenge from QPR's Spanish midfielder Jordi Lopez.
Referee Graham Scott initially pointed to the spot but changed his mind after consulting his assistant and instead awarded a corner.
Jubilant Norwich boss Bryan Gunn declared: "I'm relieved and proud. The players carried out what we asked of them.
"They could have let their heads drop after the penalty decision but they battled and got their just reward.
"It was a passionate, committed and battling performance. We knew QPR were a big, physical side that would ask us questions and the wet conditions also made things difficult.
"A lot of people have written us off and I've explained to the players that we might need to have a siege mentality. Hopefully, this result proves that we will battle.
"One question I asked the players was whether they'd thrown the towel in, and I think this performance shows that they haven't."
Fotheringham, meanwhile, is expected to join Preston on loan and Gunn conceded that the player's departure is "an option."
"I'll have a chat with Mark," Gunn added.
"It was decided that he wouldn't be in the travelling party for this game and we'll now discuss where we go from here."