Though the Premiership side still have one Group D fixture left, they will finish below the top two places.
McIntyre led County to their first League Cup triumph against Hibernian at Hampden in March's final.
"We played right into their hands by making gilt-edged mistakes," he said after the 3-2 loss at League One Alloa.
"We were nowhere near good enough. The performance was embarrassing.
"I can only apologise to our fans who made the journey down tonight."
The eight group winners and four best runners-up will progress to the second round and Alloa's win took them top of the section.
However, McIntyre felt County should have had a penalty when Jason Marr challenged Alex Schalk with the score 3-2.
"The referee has made the worst decision of the night," said McIntyre.
"It's a stonewall penalty on Alex Schalk. I have looked at it several times.
"It was a poor, poor decision at a crucial time in the match where I thought we had the ascendency and looked as if we were pressing for the third goal.
"It was a big moment in the match."
Jim McIntyre described Ross County's League Cup defeat by Alloa Athletic as "embarrassing" as the holders were knocked out of the tournament.