The Russian club were sanctioned by Uefa on Wednesday over abuse aimed at Manchester City midfielder Yaya Toure in the sides' Group D clash last week - won 2-1 by the Premier League outfit.
Toure reported the chants to referee Ovidiu Hategan, who requested a message to be sent to supporters over the public address system asking them to stop. However, this was not done, resulting in the sacking of Uefa's venue director for the game.
CSKA will play the next Champions League game at the Arena Khimki, against Bayern Munich on November 27, with a section of their stadium closed - the set punishment for a first offence of fan racism set down by Uefa in new guidelines that were created in May.
A second offence would result in a full stadium closure, and a third could lead to a points deduction or expulsion - which Carlisle believes is too long to wait.
"I think that, in a situation like that, it should be tournament expulsion," he told Perform.
"That might sound dramatic but the reason I think that is because if that incident happens here and it's 100 yards in any direction from the football ground, and the person, or group of people, committed that offence, they would be arrested and prosecuted.
"So, I don't understand why, just because it's in a football ground, that different rules are at play.
"I don't think that the sanctions we have in football at all, are anywhere near adequate."
Carlisle was happy to see Uefa stick to their guns and reprimand the Russian club, although he called for tighter measures to be established, in order to effectively prevent future incidents.
He explained: "I'm happy in so far as they've actually done what they said they would do and investigated it efficiently, reached a decision and sanctioned according to the guidelines they've got there.
"Uefa have acted appropriately in this situation."
However, when asked if the punishments were enough, he added: "No, nowhere near, you can you be happy only in so far as Uefa have acted from the incident and investigated it accordingly.
"The extent of the sanctions in my opinion are nowhere near enough because there is no way the consequences will be felt by the perpetrators.
"Closing a section of the stadium will just mean they will sit in another part of the stadium for one game and there is no reason for CSKA Moscow or the fans who committed the offence to address their actions or address the issue at hand."