Jarvis, who finalised his move from Wolves on Friday, made his debut on Saturday, impressing despite the club's 3-0 loss to Swansea, with Allardyce saying he showed promising signs.
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"It's about us continuing to supply him with the service he likes," Allardyce was quoted as saying by Sky Sports.
"When you give him that service he is exceptionally talented in the final third.
"I think their full-backs just couldn't stop him crossing the ball when he did that little trick where he drops the shoulder, because he is so good with both feet.
"It's about us giving him the service to show that ability. Unfortunately he faded a bit in the second half but he was very good in the first.
"He tired a bit but he has had such a big week and he will get better and better as he settles in with the players; as he learns to understand them and they learn to understand him."