The Seagulls host Leeds at the Amex Stadium on Friday evening as Poyet's troops look to get back to winnings ways following two defeats in the last six days.
Last weekend's league loss to Leicester and the midweek Carling Cup reverse against Liverpool dampened spirits after the promoted side began life back in the second tier with five wins and a draw from their first six games.
But Poyet will be hoping to get back on track when he welcomes his former employers to the south coast.
Poyet was assistant to former Chelsea team-mate Dennis Wise at Elland Road when the West Yorkshire club started the 2007-08 season on minus 15 points, and the Uruguayan told Brighton's official club website: "It was a great experience for me.
"It was one of those opportunities that someone should pay to experience, but I was getting paid to do it instead. I was getting paid to learn which is magnificent and helped me a lot.
"I had a great time at the club and I learned so much. I believe I had a great connection with the fans, even though I was ex-Chelsea - which is not easy.
"I can feel that connection when I go anywhere in England and meet Leeds fans. It's a very good club with terrific supporters. At home they act as an extra player, and away from home they always take their full allocation.
"They always want their team to win and they are always supporting their players right until the end.
"It's a club which deserves to be in the Premier League again one day."
Poyet is impressed with the way Brighton have closed the gap to Leeds in recent times, and is keen to put on a good performance in what will be his 101st game in charge.
He added: "It was scary how much better than us they were a few years ago and to try and beat them on Friday will be great.
"Hopefully we can show how far we have come as a team."