Neither side could break the deadlock at the Amex Stadium as players from both teams struggled for quality in the final third of the pitch.
"I was expecting to win today. We definitely lost two points today and two last Saturday," Poyet told reporters.
"Don't take anything away from my players, we deserve to be where we are. If I could ask for any more it would be in terms of quality in our final ball. At part from that, it was all there."
The result leaves Brighton sixth in the Championship, two points clear of Leicester City in seventh, outside the playoff places.