Loftus-Cheek was speaking from England's training camp after his surprise recall.
He said of Allegri's appointment this season: "He's a very intelligent coach. He's very experienced and has won a lot in the past.
"We were very excited when he arrived this summer and hope to achieve great things under his guidance."
On playing in Serie A, the former Chelsea midfielder also said: "I'm definitely used to playing in the high temperatures here in Italy now. Football is different, and it's good to experience different styles of football to gain useful experience for tournaments.
"I think all of this adds to your experience as a player—your ability to handle different situations, different scenarios in a match—and it can only be helpful. In that sense, I'm grateful to have this experience."