"We've learned that at our best we are up with the best crews in the lightweight four field," Grant, a three-time winner of the world lightweight single scull title, said.
"That's a real positive for us and even though we are all disappointed at not making the A final we definitely feel that we are tracking well for the qualification regatta."
The news was not so good, however, for the other New Zealand crew with Olympic ambitions, the men's eight.
The eight finished fifth and last in their repechage in a race in which the first four advanced to the final.
New Zealand were third at the 500m mark before drifting back to finish 1.76s behind fourth-placed Ukraine.
The eight's job is tougher than the lightweight four's, they must win the Lucerne event to progress to London. Right now that's looking a tall order.
The only other New Zealand crew in Belgrade, the heavyweight coxless four, had a poor day. New Zealand has already qualified for the Games in the discipline, but could do no better than fifth in the B final last night.
In the B final New Zealand managed 6:01.00 - having been an encouraging third at the 1500m mark - to finish behind Romania (5:57.79), Russia, Germany and Italy.
Those three crews will be joined by the remainder of New Zealand's Olympic-bound crews for the Lucerne regatta.
New Zealand have 11 crews confirmed for London.