Lisa Gibson put Paul Metz's side ahead and the score remained deadlocked at half-time before Greece accelerated away to secure a 13-7 victory.
And with Olympic champions USA up next, it doesn't get any easier.
“It is a pity we couldn’t adjust well to the different plan the opposition made," said Metz.
“We started well but the Greek team found solutions for our players and we couldn’t adjust.
“Next match we will make a plan to win as always, we're looking at each individual to find out the three or four things we can improve.”
Great Britain are making their first appearance at this level in a decade and captain Rosie Morris believes the side have improved since their eighth place finish at last year's Olympics.
“I think we really underperformed in this game, we made too many mistakes in defence that we know we shouldn’t be doing. We know what we need to work on for the next game," she said.
“We scored a lot of goals and that is something we have improved on since Paul Metz came in as coach so that is positive.
“We got our game right in the first half, we were equal with them at half time but we need to sort out our second half and the mistakes.”