The former England duo have played a major role in taking Brighton into the npower Championship play-offs since moving to the south coast on loan.
Left-back Bridge will be out of contract at Manchester City at the end of the season, as will Stoke centre-half Upson, but Poyet knows he will only be able to sign them permanently if Albion can pay top-flight wages.
"Being totally honest it is a matter of finances," he said.
"Everyone knows the financial difference, it's why the Football League and the FA wants the Championship play-off final to be the last game of the season, because it is the biggest prize.
"The difference for the team that goes up is so big that it will for sure influence it.
"If for some reason it goes wrong then they would have to make a big effort to stay here - more than us.
"It's a unique situation at the moment. The players have played fantastic knowing 10 of them are out of contract in the summer. It's strange to be at this moment in time with so many players out of contract."
If they are to achieve promotion the Seagulls must first negotiate a two-legged semi-final against their fierce rivals Crystal Palace, starting at Selhurst Park on Friday night.
A total of 14 people were arrested following the two meetings between the teams earlier in the season, and Poyet wants the matches to be remembered for the football.
"We all need to make sure the message is clear, it's a football game," the Uruguayan added at his pre-match press conference.
"People will be singing against each other, some nice banter, but nothing more. It's a football match, there are plenty of things more important.
"Of course the winners will be delighted for two reasons; reaching the final and beating their arch rivals. But it's a football game."