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Rovers manager Graeme Souness refused to blame his strike pair for passing up numerous chances which he believes on another day would have produced handsome dividends.
"We missed some golden opportunities and the chances fell to the right people but I am not going to criticise them," he said.
"We think we have dropped two points because I think we did enough to win the game.
"It was never going to be easy coming to Sunderland. It was a different challenge to the Worthington Cup semi-final against Manchester United at Old Trafford on Wednesday night and I knew Sunderland would get chances and we had a bit of luck when they hit the post."
It was left to central defender Jody Craddock to come closest to breaking the deadlock, his left-foot shot in the 69th minute from a Julio Arca corner beating goalkeeper Brad Friedel only to come back into play from the woodwork.
Kevin Phillips completely missed his kick in front of goal in the 33rd minute from a Tore Andre Flo flick-on, but chances were few and far between for a disjointed home side boosted by the return of goalkeeper Thomas Sorensen.
The Danish international replaced Jurgen Macho, who has improved beyond all recognition when deputising for the last three months while Sorensen recovered from a dislocated shoulder.
And Sorensen repaid his manager's faith by denying both Yorke and Cole with breath-taking second-half saves from point-blank range as Rovers threatened to inflict another demoralising defeat on the Black Cats.
"A point is better than none," said Wilkinson. "We finished a lot better than we started and I can't fault our work ethic or fitness.
"But we did not take enough responsibility on the ball and in our position people have to take responsibility."