But that drought ended on Saturday with a four-point victory over the Kiwis at the DW Stadium in the Third Test.
The win brought a combination of delight and relief for Graham, one of the veterans of the England set-up, who made his debut for Great Britain way back in 2006.
“It’s a mixture of emotions in terms of your celebrating the win but also the pressure release as well,” the Bulldogs forward said.
“I’ve been there and obviously bitterly disappointed in the last two years but that’s rugby league.
“I think when two good teams come together, or four teams, there has to be a loser.
“A lot of people don’t look at that in sport.
“They just see the winners and they over-analyse what happens in defeat.
“Credit to both teams and credit to us for getting the series win.”
“And against a side like the Kiwis,” the front-rower added.
“People will write and say that they were missing some players but so we were, and that’s what happens in international football.
“That’s what happens in international in different sports as well.
“You can only beat what’s in front of you – you can only play with the players that are available.”
“For me, for the people in charge of England rugby league, it’s a bit of a no-brainer,” the 30-year old said.
“If Steve wants the job I can’t see any reason why he shouldn’t continue in the job.
“Last year we were very close and this year obviously we’ve had a series win.
“So it would be a very odd decision I think to change that.
“I don’t believe there’s a need to change and obviously Macca’s done a great job.”