Rocco Quinn gave County the lead in the 20th minute with a deflected drive, but Michael Ngoo levelled 11 minutes later.
Hearts got their noses in front when Jamie Walker netted just after the hour mark, but right at the death Iain Vigurs fired home from close range to salvage a point for the hosts.
Adams said: "I thought we played very well in the first half and deserved to be 1-0 up. It was another good point for us. I was just delighted with the performance and the point.
"We are trying to catch Hibs and Aberdeen, we are a point closer today and we still have a game in hand over both sides. We've done exceptionally well."
Asked if he was surprised by how well his side are doing, Adams added: "I thought we would do well, we have a good group of players here. We knew what were going to do in January, change things about. We had a steady footing in the SPL, we knew what a good side we could be and we've shown that."
In contrast, Hearts manager John McGlynn felt it was two points dropped.
He said: "County put us under pressure right to the end but I felt we merited all three points. Two points have slipped away but I've got to be positive, it was another very good performance from us. We played some great football. I thought County scored against the run of play and we had chances to go in front before that.
"We showed character, I always thought we would get back into the game because we were playing well enough. It was a great individual goal from Michael.
"I thought we were well on top and we got another goal when Jamie Walker put us 2-1 in front. We had chances to go 3-1 up that would probably have killed County off but unfortunately we weren't able to defend right to the end."