He said: "It has been magnificent being able to reach the final. Today we did not perform. That is not taking anything away from Dundee United.
"To come to a final you always want to win. You never want to be the loser. We take huge satisfaction of doing so well this year.
"My players have been great all season. Dundee United have quality players. They scored three good goals so you cannot take anything away from them.
"There were 20,000 from the Highlands. That is testament to the players. Year on year we have improved."
Adams refused to criticise keeper Michael McGovern for the opening goal.
He said: "I do not want to talk about individual mistakes or anything like that. Over the season players have done very well for us. They have made mistakes but done things that are positive for us.
"The first half was not particularly good as not much football was played and I always felt the first goal was going to be vital."