Adams was delighted with the display in the Co-operative Insurance Cup third round, as County lost 2-1 after extra-time against their top-flight opponents.
"I thought we were brilliant to start with and played exceptionally well," Adams said. "We created a number of opportunities, more in the first half than we have done all season. To take Dundee United so close was pleasing.
"But you are always disappointed when you haven't won the game."
The only complaint from Adams was over the penalty decision by referee Craig Thomson which gave United the opening goal in the 61st minute.
David Goodwillie won the penalty on the hour mark when he was adjudged to have been fouled by Paul Lawson, and converted it himself.
However, the County boss claimed there was a shove on Gary Miller by Goodwillie prior to the incident.
Adams said: "I've seen the replay for the penalty on TV. Unfortunately the referee doesn't see the foul on Gary Miller in the lead-up, so I'm disappointed from that point of view. You have to be 100 per cent sure about your decisions you are in that situation, you have to see it to give it."
He added: "It was a definite foul on Gary Miller so it should not have got to the next stage. It is very difficult when you are a referee and I think he has reacted to shouts and given the penalty kick.
"These things go against you, but I thought we were great. I thought we had a good chance to go through and unfortunately we didn't make it."
Iain Vigurs hit an 87th-minute equaliser but United grabbed victory after Scott Boyd scored an own goal after 101 minutes.
United manager Peter Houston said: "We knew before the game we would have to fight for everything.
"Some good teams have come up here over the last couple of years. I'm over the moon just now, the main thing for me was to get through."