Bristol are seven points behind 11th-placed Worcester with five games to go after Sunday's 41-24 loss at Sixways.
Back in the top tier after seven years in the Championship, Bristol have won just three league games this season.
"There is a long-term plan in place. If we don't succeed in staying up, nothing changes," Booy told the club website.
"Results like Sunday's defeat against Worcester are difficult for all of us to take - supporters, players and staff. But in the bigger picture, these are short-term set-backs.
"The vision and ambition is clear and make no mistake, we will be a hugely successful rugby club in the future."
Bristol host Gloucester on 24 March before facing all of the Premiership's current top-three sides - Exeter, Wasps and then Saracens - prior to a final-day visit of Newcastle to Ashton Gate.
Speaking after Sunday's loss to Worcester, captain Jordan Crane told BBC Radio Bristol: "We are going to keep fighting. It is by no means done or finished.
"There is plenty of rugby left to play. All we can do is give everything we have got for Bristol.
"It was built up as a season decider but, even if we had won (at Worcester) it wouldn't have meant we were safe."
Bristol, who sacked former director of rugby Andy Robinson after losing their first 10 games of 2016-17, have been led by interim head coach Mark Tainton since November, with new boss Pat Lam to arrive from Connacht at the end of the season.
From next season, only the Championship winners will be promoted to the Premiership, after the play-off system was scrapped.
Earlier on Tuesday, Bristol announced the signing of Ireland fly-half Ian Madigan from Bordeaux from the summer, regardless of which division they will be playing in next term.
Nothing will change at Bristol if the Premiership's bottom club are relegated back to the Championship this season, says chairman Chris Booy.