Poyet's men were denied victory by a stoppage-time equaliser in a 2-2 draw at Nottingham Forest on Saturday and the Uruguayan was expecting them to make amends against the Addicks.
Brighton were twice denied in stoppage time as Vicente rattled the crossbar and Gordon Greer hit the post.
"I was expecting to win today. We definitely lost two points today and two last Saturday," he said.
Brighton remain in sixth place in the Championship and Poyet made it clear he felt his team deserved to be in a play-off spot.
He said: "Don't take anything away from my players, we deserve to be where we are.
"The game was not difficult to analyse.
"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.
"It really was one-way traffic and it was a great point for Charlton. I had a feeling they would be defensive and solid, and I can't remember the last time I didn't make a change during a game."