Hall, 18, came on in the second-half of the 3-0 win over Fulham after impressing in the Capital One Cup success over Crewe earlier in the week. The England Under-19 international told West Ham's official website he hopes to remain in manager Sam Allardyce's plans.
He said: "I just need to keep doing what I do and, if the ball comes to me, remain composed. I will continue to work hard on the training ground and I am sure it will happen. "I am very happy after making my Premier League debut - the lads helped me through it and I also played last Tuesday in the Capital One Cup.
"We put in very professional performances in both games and I am just grateful for the opportunities. It is also great for the other lads in the youth set-up too see someone make the step up."