England ended their eight-year drought for silverware with a tense 20-16 victory against the Kiwis at the DW Stadium in Wigan on Saturday.
Cooper played in all three Tests off the bench, after making his international debut in Leigh against France prior to the series.
“It’s amazing,” he said.
“To make your debut, play for England and win a series, it’s not been done too many times. I’m just over the moon to be part of it, and [with] a great group of lads as well.
“I think we deserved it. We battled hard through those three games, we had to defend a lot and showed a lot of character so I just think this is just the start for English rugby league.
“I think we needed to get a series win out of the way and hopefully we can kick on now.”
New Zealand made a late rally in Wigan, scoring two tries in the final six minutes to make it a nervous ending for the hosts.
But Cooper insisted that the result at that stage was never in doubt.
“It was one of them where you’re trying to get in front of them, but you don’t want to give a penalty away because it gives them field position,” he said.
“It’s hard to play like that and they showed a lot of skill, in that weather. They tested us, as we knew they would. But we hung in there and once we got a bit of breathing space they didn’t put us under too much pressure. It was never in doubt I think.”
Cooper said the series win is a great omen ahead of the Four Nations next year.
“It mixes it up,” the 27-year old said.
“Regardless what people say about players missing or whatever, we’ve had to show our character in these three Test matches.
“We were in a shared position for most of them. There’s a lot of real positive signs for us moving forward and shown we can beat the number one team in the world.
“Where that puts us, I don’t know, but we’ll certainly be confident going into the next series next year.”