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.
The result saw the Teessiders drop to 11th in the table, behind QPR, with four games remaining.
9. Neeskens Kebano - 5
Inviting cross led to Boro’s equaliser but found it tough to link Boro’s attack and midfield. 5
Photo: Getty Images
10. Duncan Watmore - 6
Made a few probing runs and forced a few saves from QPR keeper Seny Dieng.6
Photo: Stu Forster
11. Yannick Bolasie - 7
Erratic at times but was Boro’s biggest threat. Headed goal got his side back in the game. 7
Photo: Stu Forster
12. Marvin Johnson - 6
(for Fisher, 55) Gave the side some extra drive on the left in the second half. 6
Photo: George Wood