Messi watched from the stands as his Barca team-mates earned a 2-0 Group B victory over Italian visitors Inter at Camp Nou on Wednesday.
Icardi and Inter were looking to take advantage of Messi's absence, with the Barca captain and five-time Ballon d'Or winner sidelined due to a fractured arm.
But Inter left Barcelona empty-handed following goals from Rafinha and Jordi Alba, much to Icardi's frustration.
"I think the difference was in the first half, where we didn't play up to Inter standards. We left too many spaces and allowed them the initiative," Icardi told Sky Sport Italia .
"In the second half, we did better and forced Barcelona to misplace passes, but could've done more to make the most of the situation by finishing off the chances.
"I am not very happy with the performance, because we could've done well from the start and instead were pinned back. We've got to put in a great shift at San Siro and get points to go through.
"We knew that we were up against world class champions who have won everything over the years. If you allow them a goal, it becomes difficult to recover."
The defeat ended Inter's perfect start to Group B, with Luciano Spalletti's side now three points behind Barca heading into the reverse fixture at San Siro on November 6.