The Seagulls moved to fourth place in the Championship following their goalless draw with the Posh as neither side could break the deadlock at London Road.
Poyet told the club's official website: "We got another point, we are up to fourth and we have got to be happy with that at this time of the season.
"We knew it would be difficult because Peterborough are a good side and in very good form. We did the basics well."
Next up for promotion-chasing Brighton is a home game at the Amex Stadium against Blackpool.