We edged the first half of a game of few chances but Steve McClaren's men got on top after the break, forcing two fine saves out of Kasey Keller from Boudewijn Zenden and Gaizka Mendieta.
A late rally produced chances for Stephane Dalmat and Helder Postiga but Mark Schwarzer in the visiting goal wasn't seriously troubled.
The draw stretched our run to five unbeaten games, four in the Premiership, keeping four clean sheets in that time.
"It was a nearly game for us, a few nearly men out there," said caretaker boss David. "But in terms of spirit I can't fault them.
"Halfway through the second half we could have lost it but we were strong and we kept fighting until the end.
"We had rhythm and ascendancy in the first half but we lost that in the second - although quite frankly I thought it was an exciting game even if it wasn't the highest quality.
"We didn't keep calm in the second half and we got a bit too anxious.
"I am not down about that point. Middlesbrough are good opponents and all my reports told me they had been playing well with little fortune, and they deserved their point for sure."
David Pleat described Sunday's Premiership stalemate against Middlesbrough as a 'nearly game' for us.