Having rallied back from 7-0 to tie the game at 10-10 thanks to Charlotte Barras' converted score but Kelly Brazier's penalty ensured New Zealand won their fourth straight World Cup.
And Spencer was at a loss to explain why the Kiwis continue to hold a jinx over 2010 RBS 6 Nations champions England in World Cup competition.
He said: "We're all absolutely gutted that we lost and lost by only three points. I've got mixed emotions.
"I'm really proud of the girls and what we've done not only in this tournament but for the last couple of years but I'm absolutely devastated that we didn't win.
"We beat New Zealand in November and we were confident we could do it again. We're really proud of our defence. The first 20 minutes was like a New Zealand onslaught but we kept them away from our line and they didn't score which was awesome.
"Unfortunately we just didn't quite get enough time in their half and couldn't keep hold of possession."
England vice-captain Katy McLean was quick to echo her skipper's sentiments.
The fly-half missed two first-half penalties and was inconsolable at the final whistle.
He said: "At first it didn't sink in that we had lost as we had such belief in our team that we could come into this tournament and win it.
"We got so close and sometimes that makes it harder to take because you get that close to your ultimate goal and then it slips away.
"All credit to New Zealand as they played an outstanding game tonight. It was a good game of rugby but devastated is the only word I can use for how I feel.
"I'm devastated for all our squad and for our staff. But it was a really good game and hopefully it's lifted the profile of the sport."