O'Riordan suffered a dislocated shoulder during Bristol's first home league loss of the campaign - a 12-7 reversal to the improving London Irish, who had full-back Delon Armitage sent off early in the second period.
With Perry likely to be involved for England against Wales next weekend, Bristol head coach Richard Hill will summon 23-year-old Greg Nicholls for a tricky encounter at play-off rivals Saracens after O'Riordan joined Matt Salter, David Hill and Brian Lima on the casualty list.
Hill said: "We have to win our two remaining home games against Worcester and Northampton to stay in the top four.
"And the most we can hope for from next Sunday's game at Saracens is a (losing) bonus point, as we will probably have to keep some of our senior players back for the week after against Northampton.
"We could have won this game. It was a very close thing. but just didn't finish off where we should have done."
Irish overcame the loss of Armitage - who was dismissed by referee Tony Spreadbury following an off-the-ball skirmish with Bristol wing Lee Robinson - to make it four successive Premiership wins, even though they were without England pair Mike Catt and Shane Geraghty.
Riki Flutey and Barry Everitt, who will play for Wasps and Northampton respectively next term, each kicked two penalties.
Exiles rugby director Brian Smith said: "A month ago, we said that to have a chance of the play-offs we would have to win six of our last nine games.
"We have bitten off one week at a time and got ourselves a bit of momentum, but we can't get too carried away because we face Wasps next, and that would be a big prize for us."