Captain Muhammad Imran, who converted a penalty corner to put his side ahead after 31 minutes, said Pakistan created numerous chances in the attacking quarter but failed to capitalise on them.
"We played well but unfortunately we missed our chances and we're working on that," he said.
Britain were more clinical in the second half, taking all three points through second half goals to Mark Pearn and Richard Mantell.
However, Pakistan team manager Khawaja Junaid said the Green Shirts, who shocked Australia 4-3 in Perth last month, showed they were making progress.
"We are still in the tournament... we played good hockey and we are not demoralised," he said.
England were runners-up to Australia at last year's event and, because the tournament in Auckland is a lead-up event for the Olympics, its players form part of a combined British team this year.
Hosts New Zealand play Germany in Pool B later Saturday, while South Korea face the Netherlands.
Australia survive Spanish scare
Australia made a stuttering start to their Champions Trophy defence with a 3-2 win over Spain.
In men's hockey's last major tournament before next year's Olympics, hot favourites Australia needed two goals from inspirational skipper Jamie Dwyer to down the committed Spaniards.
Dwyer admitted the Kookaburras, chasing an unprecedented fourth straight Champions Trophy, failed to live up to their billing as the world's top-ranked team and raging favourites to claim Olympic gold at the London Games.
"We were very passive, we should have been a lot more aggressive and we allowed their ball carriers too much time and space," the four-time world player of the year said.
"We definitely didn't play to our potential and we're probably lucky to get the result in the end. There's no real excuses."
Spain peppered the Australian goal as they dominated the opening skirmishes but a well-taken short-range goal from Dwyer against the run of play put the reigning champions ahead after 10 minutes.
The Spaniards, who have only beaten Australia three times in 22 Champions Trophy clashes, hit back 15 minutes later when an off-balance Jorge Dabanch stayed on his feet long enough to fire a shot past goalie Andrew Charter.
Eduard Tubau shot Spain into the lead two minutes later, when he split the Australian defence to again beat Charter.
The Kookaburras wrested control of the second half, with Dwyer netting the equaliser just after the break and a penalty corner conversion from Desmond Abbott sealing the win.
Spain coach Daniel Martin said the performance was a confidence booster for the Beijing silver medallists as they look to bounce back from disappointing recent results.
COMMENTS (3)
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I am myself is a hockey player commenting on other player is very easy but playing on the ground is very different. We can only support our team weather it play a bad or good game it is the game on that day how the player played it is not always that we will win only other team are there to win also. We just need to pray and support our team.
This was an ideal match to bag 3 points in a tough group. Now we have to beat the top teams to get in the top 2!
Not the start we expected after holding the Olympic gold-medalists in the warm-up but still let us hope we learn from this encounter and go on to take our chances in the upcoming encounters...Best of luck Greensticks!