The 18-year-old scored the Railwaymen's second goal as they beat Southend United 2-0 at Wembley on Sunday.
"What an unbelievable feeling to start and score at wembley! Stuff of dreams," he wrote on Twitter.
Clayton, who was named as the man on the match, added: "Unbelievable feeling to get MOTM award".
Crewe have now won at Wembley on three occasions, adding to last season's League Two playoff triumph over Cheltenham Town and their Division Two playoff win against Brentford in 1997.