It looked like the Teessiders had done enough when Gary O'Neil put them ahead after 58 minutes, but Tony Mowbray's side were stunned by two late goals from Shaun Harrad which saw them eliminated from the competition.
Mowbray said: "Last-minute goals are killing us. It happened at Elland Road last weekend and it's happened again here.
"If we could have taken a better share of our chances it wouldn't really have mattered. They wouldn't have gambled like they did because they would have been two or three goals down and out of it.
"But when a team is only one goal down, they'll always put you under pressure in the last few minutes. It's another example of one goal never being enough.
"I don't even think it was a case of them putting us under any sort of pressure. It was just two isolated incidents."