The Tigers claimed a 1-0 Northern Counties East League Premier Division success at Eccleshill thanks to substitute Matt Sykes’ volley on the hour.
Poulter, stepping in for holidaying manager Craig Denton, said: “We played against a big, strong and physical side who kept many behind the ball, so we had to be patient.
“What I liked about us was that we didn’t give up.
“We kept playing the right way and we got our reward.
“There are definitely things we need to work on and improve, but it is still early in the season.
“The lads still need to understand that we’re working hard, but it’s stuff in between we need to work on.”
Tigers striker Craig Mitchell saw two chances go begging within as many minutes — first he headed Steve Woolley’s inventive cross just over before striking the bar from the edge of the area after turning his man excellently.
The Tigers broke the stalemate when a cross was headed on for Sykes to hit a fine left-foot volley into the far corner.
Poulter said the Tigers’ substitutes — Sykes, Ross Goodwin and Kyle Jordan — made a good impact.
“The bench was on my mind coming up to the game as all of them I could put in without an issue.
“In the game I thought attacking wise we needed something a little bit different.
“They were obviously sat back and we wanted to be more direct and someone who could run with the ball — and Sykes has done that.
“He gave their full-back something to think about and dragged them wider to create more space inside. I’m very happy with how he played.”
Poulter also praised the travelling supporters. “The fans were unbelievable. The singing and clapping at the end made the lads feel proud to pull the shirt on,” he said.