The Grecians dominated throughout against the league leaders but could not find a way past Gills goalkeeper Stuart Nelson, Jamie Cureton missing three great chances for City.
The point sees Gillingham stay five points clear from Burton, who moved into second place after Port Vale lost at Bristol Rovers.
"They are just behind us in the league so this is a big result," said Allen. "We all left home at 6am to make sure we got to the ground for eight because of the Siberian blizzard in Gillingham. It took ages to get down here.
"Did we play great individually? Not really. Did they dig in? Yes.
"Our goalkeeper had one shot to save in the first half and one in the second half. It is a clean sheet and a good point.
"They are all committed, that is why I always change it around and give other people opportunities to play. They have a respect for each other and I trust all the players to play.
"We played some good football. We tried to keep the ball and move it about because they are not an easy team to play against down here because they keep possession - that is the name of their game.
"So we had to be patient at times, you can't always win it back quick. There were spells in the game when Exeter had a lot of the ball but we did well."
- Sports & Recreation
- Bristol Rovers
- Jamie Cureton
- Stuart Nelson