The managerless south-coast club would have been without 12 players through injury and suspension and were expected to include three loan players signed barely 24 hours before the League One contest.
But the torrential downpour that lashed Bristol left standing water on the pitch at the Memorial Stadium and Trollope admitted referee Kevin Friend had little option but to call the match off.
He said: "Brighton are unsettled at the moment with their managerial position, as well as injuries and suspensions and new players coming in.
"You never know how that would have worked out - and unfortunately we never will. But I would have said that we had a good chance of winning the game, and when they return in a few weeks time it will obviously be a different story as I think they will have a new manager in place then and a more settled side.
"We would have liked to have played but you never want a pitch that is going to make the game a farce. The surface would have made it impossible for both teams."