Having signed in a swap deal from Arsenal on Monday, Sanchez made his United debut in Friday night's 4-0 FA Cup fourth-round win at Yeovil.
"He is not bad, is he? Not bad for a little man," Carrick told MUTV. "He is going to be a terrific player.
"He is a proper Manchester United player and it's great to have him here. He is so exciting and so dynamic.
"He's always looking to create opportunities, to play forward, and the fans are going to enjoy watching him.
"Hopefully, we will enjoy playing with him."