The Black Cats enjoyed the best of a low-quality game at Upton Park but the Premier League struggler's poor finishing let the team down as the match drifted to a 0-0 stalemate.
The Black Cats remain bottom of the table with just two Premier League wins all season after they were unable to break down a stubborn Hammers defense at Upton Park.
Poyet's side are now five points adrift of safety heading into the vital Christmas fixture period but the Uruguayan believes that they did enough to win.
"I am not happy with the point because we were definitely the better team," he told reporters. "We definitely deserved to win but we didn't get any breaks. I think we had 19 shots. How we didn't score, I don't know.
"When you play like that you need to win but I am pleased with a performance like that away from home."
Sunderland host Norwich City in the top flight on December 21 as they look to close the gap on those above them and Poyet has made it clear that he would take a victory by any means.
"I'm just waiting for the ugly [win]; we don't get those ones either," he added. "Even when we play well and deserve to win, we don't."