Will Hoskins headed Rovers in front but Chris Sedgwick, Tommy Miller, Gary Teale and Jermaine Johnson put Wednesday in control.
Hoskins struck again, but substitutes James O'Connor and Paul Heffernan replied for Wednesday.
Trollope said: "We had a difficult two-and-a-half-week break because of the bad weather but to me that's not an excuse in any way.
"We caught Wednesday on a good day, our goal spurred them on straight away to some very good things but we weren't good enough defensively to cope. We're bitterly disappointed. We came with a belief, wanting to attack - you could see that from the opening spell and our goal. But then, from a coaching point of view, we needed to be solid, make good decisions and be defensively right for the next spell.
"We looked quite good going forward at times - especially in the second half - but defensively we were poor from front to back. It was a cracking game for the neutral but we have a lot of work to do."
Source: PA
Source: PA