The Gills were second best during the first half and finished the game with 10 men after Andy Frampton saw red late on for a clash with Rochdale striker Bobby Grant.
But Allen insisted his side could still have won the contest, saying: "I thought we played well in the second half after a change of formation, and we created a few good opportunities.
"But the team we were up against are playing with a lot of freedom, playing with three up on the halfway line when defending corners and things like that. You can afford to do those sort of things when you're mid-table.
"It gave us different things to think about and different things to do but I thought the players responded magnificently in the second half and in the end I felt we were unlucky not to win it.
"I've spoken to Andrew (Frampton) and you couldn't get a more honest, decent bloke than him and he's said he never touched the player and that the guy has just gone down holding his face. I didn't see it but we'll have to take a look at that and keep it internal. If there's something to be said to Andrew then it will remain private.
"Rochdale's goal came off an error from us and these things happen over the course of a season. I'm certainly not going to apportion blame."
A defensive mix-up between Gills defender Leon Legge and goalkeeper Stuart Nelson paved the way for George Donnelly to fire Dale into a 12th-minute lead, with Danny Kedwell heading level shortly after the break.