Jo Kuffour's 71st-minute deflected volley decided the outcome after Northampton goalkeeper Chris Dunn had spilled David Pipe's right-wing cross when under pressure from Rickie Lambert and Jeff Hughes.
"We've made it clear we want a top-10 finish and there's no question of letting standards slip," said Trollope.
"We were rough around the edges in certain areas, but you could see the players were playing for the shirt and that's what I've asked of them.
"We now have three strikers in double figures for the season and the top scorer in the division, which suggests failings in other areas.
"I think that was true in the first half of the season when we had key defenders out injured. But in the second half we have been much harder to beat and it's something to build on."