Iain Davidson gave Dundee the lead eight minutes from the break, but County hit back strongly and substitute Gary Glen fired home a deserved equaliser with 16 minutes remaining.
Adams said: "Probably today was the worst we've played in the SPL. It was a high-pressure game for both sides and both teams looked a wee bit nervous and didn't do the things they do well."
He added: "After 37 minutes, we lose a goal from a great strike by Davidson and we have to get ourselves back in the game.
"In the second half I thought we created a lot of opportunities but probably didn't work (Dundee goalkeeper) Rab Douglas enough.
"He did have a few good saves and we probably should have won with the pressure we had in the second half and Richard Brittain hit the post in the last minute.
"We have gone ahead of St Mirren tonight and from a point of view of the first half of the season we've made a very good start. But in the next half we need to win more games and turn draws into wins."
Dundee boss Barry Smith said: "I thought we started really well and got our noses in front.
"We had a couple of chances early in the second half to kill the game off but we didn't take them. In fairness to Ross County they came back into it and put us under a lot of pressure.
"This is a difficult place to come and although we would have preferred the three points, a point is a good point up here. It was a good all round team performance."
- Sports & Recreation
- Iain Davidson