Boro fell two goals down after goals from Rob Dickie and Lee Wallace at the Riverside inside 18 minutes.
After a slow start Boro responded and managed to pull a goal back when Yannick Bolasie headed home Neeskens Kebano’s cross, while Rangers goalkeeper Seny Dieng was sent off in the second half.
The result saw the Teessiders drop to 11th in the table, behind QPR, with four games remaining.
Warnock will now prepare his side for Wednesday’s trip to Rotherham following another difficult afternoon when some of his players underperformed.
Boro played with a back three and wing-backs against Rangers but struggled to get a grip of the game for the opening 25 minutes.
Here’s how the Teessiders fared at the Riverside.
5. Djed Spence - 4
Struggled to get forward in a wing-back role and was beaten to the ball for QPR’s second goal. 4 Photo: Getty Images
6. Marc Bola - 6
Saw an early shot saved in the first half and tried to get forward in a left wing-back role. 6 Photo: Alex Burstow
7. Jonny Howson - 5
A few sloppy passes in midfield and QPR controlled the engine room in the first half. 5 Photo: Stu Forster
8. George Saville - 5
Saw a couple of second-half efforts saved. Was overrun in midfield during the first half. 5 Photo: Stu Forster