The contest was fairly evenly matched but County had the better of the chances and snatched victory with just two minutes left when Graham Carey was on target after a Frazer Wright error.
"We probably deserved it," said Adams.
"We put a lot of crosses into the box and were unfortunate not to get anyone on the end of them, especially in the second half.
"I thought the first half was an even affair, no team really created a lot in the first half.
"It is always difficult against St Johnstone and today was no different. They are a very good side who are in a good position.
"The team has been playing well in games but not getting the result that we deserved. We just had to knuckle down and work hard and that's what we've done.
"We've not talked about it too much, we've just worked away on the training field."
Wright rues mistake
Boss Tommy Wright felt his Saints side deserved to take something from the game.
"It was either going to be a wonder strike or a mistake," said Wright. "Unfortunately, from our point of view, it was a mistake. We should have come away with a point but we got caught.
"The final ball was poor. I don't think either goalkeeper was really worked, both defences did really well, and we deserved a point out of it.
"We should be doing better but we are in one of those runs, especially away from home, where we are getting punished for any mistake, and that was evident today."