Richie Foran scored in the fifth minute of stoppage time to earn Caley a replay after Richard Brittain had put the home side ahead for the first time in the second minute of added time.
"It was disappointing to lose a goal in that way," said Adams.
"We have to go there now for the replay and they have a good record in Inverness. They are a good side.
"We didn't do so well in the first half but we created more chances and openings in the second half. Over the piece we probably deserved to go through. We have to go to Inverness now for a replay.
"It was going to be difficult today because they are in buoyant mood having done exceptionally well in their last couple of games."