The 28-year-old moved to Villa Park from Elche in the last transfer window and has made 11 Premier League appearances thus far.
Manager Lambert paid tribute to the professionalism of the Colombia international and believes Sanchez will grow to become a vital part of Villa's first team.
"Carlos is learning very fast now and he's loving life in the Premier League," the Scot told Villa's official website.
"He's going to be a really big player for Aston Villa. The good thing about Carlos is that he never hides from anything.
"I don't mind him making mistakes providing he never hides from it. He wants the ball all the time and even if he makes a mistake he's ready to get it back.
"He's only been in this country for a short time and he still needs to adapt. But I believe in him. There's no problems whatsoever from me.
"What I like about him, too, is that he's an outstanding professional. What you see in games is what you see in training. He never slacks or stops working."
Lambert also stated his belief that Sanchez is starting to adapt to the demands of English football.
"He's coming from a country which is completely different to England and it has been a big culture shock for him," he added. "But he's played in the World Cup and he was excellent."
Villa sit 11th in the table and are five games unbeaten, with a trip to West Brom coming up on Saturday.
