Lautaro has no doubts about the potential of the centre-forward, but says expectations should be eased inside Italy.
Asked about Pio Esposito and fellow Inter striker Ange-Yoan Bonny, Lautaro told La Gazzetta dello Sport: "I know Pio better because he comes from the youth team.
"He's a serious and humble guy. Leave him alone and he'll become a pillar of Inter and Italy. Bonny also has strength and quality and is giving us a big hand."
Meanwhile, Lautaro also looked back on the Champions League home defeat to Liverpool. The Reds won 1-0 thanks to a penalty won by Florian Wirtz.
He added: "We're disappointed but not angry. Because if you lose because of a refereeing error, there's little you can do. We're sorry we threw everything away because of an injustice: if penalties were awarded or every holding, the game would never be played."