The Gills were second best during the first half and finished the game with 10 men after Andy Frampton saw red for a clash with Rochdale striker Bobby Grant. But Allen said they could still have won the contest.
"I thought we played well in the second half after a change of formation and 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," he said.
"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 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 is something to be said to Andrew then it will remain private between me and Andrew.
"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 and the visitors were let off the hook when Bobby Grant nipped in between Joe Martin and Nelson but sent a close-range finish over the crossbar soon after.
But Allen's men turned up the heat with a spell of pressure early in the second half which saw Danny Kedwell go close twice. His first effort, blasted at goal from a tight angle, was saved by Josh Lillis. Minutes later he saw a glancing header bounce inches wide of the post.
But it was third time lucky for the frontman when Matt Fish delivered an inviting cross from the right flank into the six yard area, Kedwell making no mistake with his headed finish Gillingham were reduced to 10 men for the last eight minutes of the match after Frampton was dismissed having clashed with Grant following a poor challenge by Donnelly on Legge.
Rochdale manager Keith Hill said: "I was over the moon with the way we controlled the first half, we kept possession and created opportunities and were full of energy. But for 20 minutes of the second half we looked as though we were going to fold. I'm going through an emotional rollercoaster and I found it difficult on the touchline watching us in that second half."
- Sports & Recreation