Sunderland were beaten 1-0 by West Ham United at the weekend.
Sunderland were beaten 1-0 by the Hammers on Saturday, but they created plenty of chances.
The Black Cats ended up having 13 shots throughout the contest, but they were wasteful in front of goal and Michail Antonio ultimately made them pay.
The winger cut inside and finished well to score the only goal of the game and launch his side up to fifth in the Premier League table.
The defeat means that Sunderland still remain in the relegation zone, but Parlour believes there was reason for optimism from their performance.
“Sunderland were unlucky at West Ham,” the former Arsenal midfield said. “I thought they deserved a draw because they created chances. Sam Allardyce alluded to it after the game, talking about having lots of opportunities in the second half and that they did enough to get a point.
“That will stand them in good stead going forward and they were unlucky not to go away with something from the game.”
Sunderland are currently in 19th spot in the Premier League table, but they have shown signs of progression in recent weeks.
The Wearsiders have performed well in their last four matches which they have taken four points from.
Sunderland are next in action on Tuesday evening against Crystal Palace at the Stadium of Light.