"If you're missing five or six of your players through personal circumstances, it's going to hit us hard and it does affect the integrity of the competition," Cleverley told British media.
Since players returned to limited group training on Tuesday, there have been eight positive tests for the virus at England's top-flight clubs including Watford defender Adrian Mariappa.
Watford are 17th in the league, level on 27 points with Bournemouth, who also had a player test positive on Sunday.