The midfielder returned from a short lay-off to play his part in the 1-1 draw against Shakhtar Donetsk - his second appearance in Ukraine this season after coming on for England as a late substitute in the World Cup qualifier last month.
Following his fifth start of the campaign in the Donbass Arena, the 24-year-old is aiming to keep his place for the away fixture on Wearside this weekend after paying tribute to the backroom team who ensure the players are always fresh.
"I think we're used to this as a squad now," he told MUTV. "It's part and parcel of it, all this travelling. Obviously, it's not ideal but we're all used to it now. Our recovery team and sports science guys do a really good job in turning us over ready for the next game."
Cleverley was also asked about the negative press and criticism that has surrounded the champions' start to the season.
"You try to block it out," he admitted. "If we are in this position in May, I'd be concerned but we've come back from worse than this before and I'm sure we'll be there or thereabouts. We can always do better and the results have been a bit poor recently but Wednesday was a good, solid point and something we can build on.
"There are top-quality teams fighting for it [the title] and we can't afford to lose too much ground on them."