The newly-promoted Seagulls started the season well and topped the Championship table for a number of weeks.
However, yesterday's loss has seen them extend their non-winning run to four matches in all competitions and Poyet believes their current form should act as a wake-up call.
"I thought the fans were terrific tonight and I'm sure that they are very sad. They are probably as sad as we are, if not more," Poyet told the club's official website. "We were top and now we have dropped down so we have got to be realistic.
"We can never think we are too good because someone will be there to knock us down. We need to be realistic because we are a new team.
"This is a kick up the backside for everyone, inside and outside of the club, and there are a few people who are going to wake up tomorrow morning and be more realistic than they were a few weeks ago."
Next up for Brighton is a trip to Ipswich Town on Saturday afternoon.