Boro picked up their first points of 2013 thanks to Curtis Main's 81st-minute header, while the Whites slipped eight points adrift of the play-offs.
Visiting supporters chanted: "Warnock, time to go," but the veteran manager said poor finishing was to blame.
"Unless I run on the pitch and put in the chances, I don't know what to do," Warnock said.
"It's frustrating. The last three open goals (in games against Cardiff, Wolves and Middlesbrough) are not difficult chances. I thought Middlesbrough were there for the beating.
"We had a great opportunity to take the lead and don't know how we didn't take it. We should be talking about three wins and be right in there."
On the disenchantment he added: "Its a natural thing.
"If we'd have taken that first chance they would have been chanting our names. I think we've had a good season."