That result means Adams' men have taken just five points from their last six games, with only two goals scored, but he was taking the positives from the stalemate.
"There were crumbs of comfort and we will take them and move on," he said. "I was pleased with the effort and commitment of the players. To a man they stuck to the task and we went toe-to-toe against a very good Bradford side.
"We had the better chances in the first half and I don't know how their goalkeeper has kept that one out from Popey.
"Of course Bradford had their chances in the second half, but there is no doubt if they hadn't had their cup run they would have been right up there, that's for sure.
"We've arrested the slide, it was a good clean sheet and will go again against Southend on Saturday."
Vale captain Doug Loft was sent off in injury time for a high challenge on Ricky Ravenhill and Adams says his side will miss their skipper while he serves his suspension.
"I want to see the sending off on the tape before I comment, but I've been to see the referee and he says Doug went over the top of the ball," Adams said.
"We all know Doug is not that type of player, but it looks as though we will be without him for three games. We will certainly miss him because he was excellent again."