Sri Lanka, riding on the back of an unbeaten 115 by skipper Mahela Jayawardene, wrapped up an 81-run win and will now face either Australia or South Africa in Saturday's final in Barbados.
"We were outclassed," said Fleming after his side were bowled out for 208 chasing 290 to win at Sabina Park.
"They have some big game players and a lot of heavy artillery in their bowling line-up.
"We had hoped to restrict them to the mid-200s but Mahela played a great innings and we conceded 100 runs in the last 10 overs - that was very poor.
"The margin of victory was about right."
Jayawardene had won the toss and elected to bat and Sri Lanka made the most of a wayward display by spearhead Shane Bond who finished with 1-59 off his 10 overs.
In stark contrast, Sri Lanka's opening pair Chaminda Vaas and Lasith Malinga bowled two impressive, mean opening spells as New Zealand were limited to 30-1 off the first 10 overs.
"Even if we won the toss I don't think it would have chan