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.
. MIDDLESBROUGH, ENGLAND - FEBRUARY 16: Boro player Grant Hall in action during the Sky Bet Championship match between Middlesbrough and Huddersfield Town at Riverside Stadium on February 16, 2021 in Middlesbrough, England. Sporting stadiums around the UK remain under strict restrictions due to the Coronavirus Pandemic as Government social distancing laws prohibit fans inside venues resulting in games being played behind closed doors. (Photo by Stu Forster/Getty Images)
Middlesbrough defender Grant Hall. Photo: Stu Forster
. Jordan Archer - 5
Received his chance in goal but was left exposed for both goals. 5 Photo: Alex Burstow
. Darnell Fisher - 5
Made some important interceptions early on in the right centre-back role but didn’t look totally comfortable. 5 Photo: Catherine Ivill
. Grant Hall - 7
Won some important headers against QPR fromtman Lyndon Dykes in the heart of Boro’s defence. 7 Photo: Stu Forster
1. Jordan Archer - 5
Received his chance in goal but was left exposed for both goals. 5 Photo: Alex Burstow
2. Darnell Fisher - 5
Made some important interceptions early on in the right centre-back role but didn’t look totally comfortable. 5 Photo: Catherine Ivill
3. Grant Hall - 7
Won some important headers against QPR fromtman Lyndon Dykes in the heart of Boro’s defence. 7 Photo: Stu Forster
4. Paddy McNair - 6
Allowed Dykes to cross the ball for QPR’s second goal. Helped start some attacks from the back. 6 Photo: Alex Pantling