The tourists were coasting towards their 181-run target at Saxton Oval on 139-2 in the 15th over on Monday.
However, captain Morgan holed out to Mitchell Santner to spark a loss of five wickets for just 10 runs as New Zealand moved 2-1 ahead in Nelson.
"I think that's one that got away from us," Morgan said in the post-match presentation.
"I thought we were in control the whole chase, probably until we went three or four down - then the lack of experience in the chase possibly cost us.
"But the guys that have come in need to play more games and get in more situations like that, in order for us to find more out about them.
"I think it's great the series has been so competitive so far, we're integrating everybody into the squad, but certainly we feel that's one that slipped away.
"The game plan remains the same. Everything about what we do is positive, smart, aggressive cricket - in the field, with the bat, with the ball - and we want young guys to come in and adapt to that.
"There are a lot of positives to take from today but, certainly moving to Napier and a must-win game to level the series, we'll need to up our game."
England lose wickets in 10 runs to hand New Zealand a 14-run win in the 3rd T20I
The hosts lead the series 2-1.November 5, 2019
Opposite number Tim Southee acknowledged the Morgan wicket swung the match towards New Zealand, but he was confident his side were always in the contest and praised Colin de Grandhomme's ultimately crucial knock of 55 off 35 in the team's 180-7.
"It showed that if we could keep taking wickets, it would get tougher and tougher for the news guys coming in," Southee said.
"I think with Morgan going they were nicely placed but we kept chipping away. It was great to see Colin come out and get a score. It's nice to win game like that, could have gone either way at the halfway mark."