Lee Bullen warned his Ayr side they will have to be far more ruthless if they want to keep pace at the top of the Championship.
The Honest Men were left to rue missed chances as clinical Caley left Somerset with all three points.
And Bullen insists his men shot themselves in the foot by giftwrapping victory for the Highlanders.
He said: "If there is ever a game that sums up how ruthless the Championship is, that was it.
"You need to be ruthless at the top end of the pitch and we weren't.
"The message at half time was this is a game of concentration because we were so far in front.
"Then we come straight out and one slip leaves us chasing the game.
"Their keeper has made a couple of good saves but we haven't worked him nearly as much as we should have. That's the really frustrating part.
"Billy's team will play far better this season and lose but they've been better in both boxes today than us and deserve credit for that.
"It's another game for us without a clean sheet and now we need to get back on track."
Ayr racked up an incredible 20 corners - 14 of them in the first half - as they laid siege to the Caley goal early on.
Mark McKenzie fired a good chance just wide before Sam Ashford headed off the bar.
Josh Mullin had a shot deflected wide as the pressure mounted before United blew a golden chance just before the break.
Ashford did brilliantly to retrieve possession on the byline and when he cut back for McKenzie, the striker somehow pulled wide of an empty net from six yards.
And Ayr were made to pay a cruel price for their missed chances as Caley hit the front just after the restart.
Steven Boyd's cross from the right was met by Harper whose deft header flew past Charlie Albinson.
And Caley could have doubled the lead soon after when Albinson had to deny George Oakley at point blank range.
That sparked a triple change for Ayr with ex-Caley man Logan Chalmers among those thrown on to try and turn the game.
Both he and fellow sub Jayden Mitchell-Lawson fired over as United tried in vain to find a way back into the contest.
Ayr then had huge shouts for a penalty denied in stoppage time when Mitchell-Lawson tumbled under a Danny Devine challenge but ref Colin Steven was unmoved.
