The defending champions had looked in good form as Danielle Hazell took 5-34 to restrict New Zealand to 223 despite Sara McGlashan's 88 from 90 balls.
But England fell short of their target despite 51 from Lydia Greenway and a late contribution of 35 from Lydia Gunn, with some questionable running leading to three run-outs that ultimately proved costly.
Spin bowler Hazell was disappointed with the defeat despite her positive contribution.
"We are disappointed with the result today. It was good to get out there and get some overs under my belt, yes it’s nice to make a contribution, but ultimately it’s about the result as a team," she said.
"We can learn from the result, there are things we will put into practice on Thursday and then take forward into the game on Friday [against Sri Lanka].
“There was a bit more in the pitch for the spinners today compared to the CCI ground yesterday, I think spin will definitely play its part in the tournament. We’ve got four good spinners in our side and we are all going well so there is competition for places, we’re all trying to put a marker out there and push to be in that first game."
In the day's other warm-up matches there were wins for Australia against India, Sri Lanka against South Africa - which included a recovery from 66 for six while chasing 165 to win - and Pakistan over an Odisha XI.
Group A fixtures (all venues in Mumbai):
Thurs 31 Jan – India v West Indies, Cricket Club of India
Fri 1 Feb – England v Sri Lanka, Cricket Club of India
Sun 3 Feb – England v India, Cricket Club of India; Sri Lanka v West Indies, MIG
Wed 6 Feb – India v Sri Lanka, Cricket Club of India; England v West Indies, BKC
Group B fixtures (all venues in Cuttack):
Thurs 31 Jan – Australia v Pakistan, Barabati Stadium
Fri 1 Feb – New Zealand v South Africa, Barabati Stadium
Sun 3 Feb – New Zealand v Pakistan, Barabati Stadium; Australia v South Africa, Barabati Stadium
Tuesday 5 Feb – Pakistan v South Africa, Barabati Stadium; Australia v New Zealand, Barabati Stadium
Group A squads
ENGLAND – Charlotte Edwards (captain), Jenny Gunn (vice-captain), Tammy Beaumont, Arran Brindle, Katherine Brunt, Holly Colvin, Georgia Elwiss, Lydia Greenway, Danielle Hazell, Amy Jones, Heather Knight, Laura Marsh, Anya Shrubsole, Sarah Taylor, Danielle Wyatt.
INDIA – Mithali Raj (captain), Harmanpreet Kaur (vice-captain), Ekta Bisht, Amita Dass, Jhulan Goswami, Karuna Jain, Reema Malhotra, Mona Meshram, Thirushkamini Murugesan, Sulakshana Naik, Niranjan Nagarajan, Rasnara Parwin, Punam Raut, Shubh Lakshmi Sharma, Gouher Sultana.
WEST INDIES - Merissa Aguilleira (captain), Stafanie Taylor (vice-captain), Shemaine Campbelle, Shanel Daley, Deandra Dottin, Kycia Knight, Kyshona Knight, Natasha Mclean, Anisa Mohammed, Subrina Munroe, Juliana Nero, June Ogle, Shaquana Quintyne, Shakera Selman, Tremayne Smartt.
SRI LANKA – Shashikala Siriwardena (captain), Sandamali Dolawatta (vice-captain), Chamari Attapaththu, Eshani Lokusooriya, Lasanthi Madushani, Dilani Manodara, Yasoda Mendis, Udeshika Prabodani, Oshadi Ranasinghe, Inoka Ranaweera, Deepika Rasangika, Sherina Ravikumar, Chamani Senevirathne, Prasadini Weerakkody, Sripali Weerakkody.
Group B squads
AUSTRALIA – Jodie Fields (captain), Alex Blackwell (vice-captain), Jess Cameron, Rene Chappell, Sarah Coyte, Holly Ferling, Rachael Haynes, Alyssa Healy, Julie Hunter, Meg Lanning, Erin Osborne, Ellyse Perry, Megan Schutt, Lisa Sthalekar, Elyse Villani.
NEW ZEALAND – Suzie Bates (captain), Amy Satterthwaite (vice-captain), Kate Broadmore, Nicola Browne, Rachel Candy, Sophie Devine, Natalie Dodd, Lucy Doolan, Sara McGlashan, Frances Mackay, Morna Nielsen, Katie Perkins, Rachel Priest, Sian Ruck, Lea-Marie Tahuhu.
PAKISTAN - Sana Mir (captain), Bismah Maroof (vice-captain), Nain Abidi, Sidra Amin, Diana Baig, Elizebath Barkat, Nahida Bibi, Qanita Jalil, Asmavia Iqbal Khokhar, Syeda Batool Fatima Naqvi, Nida Rashid, Rabiya Shah, Sumaiya Siddiqui, Javeria Wadood, Sadia Yousaf.
SOUTH AFRICA – Mignon du Preez (captain), Trisha Chetty (vice-captain), Susanna Benade, Cri-Zelda Brits, Savanna Cordes, Dinesha Devnarain, Shandre Fritz, Shabnim Ismail, Marizanne Kapp, Marcia Letsoalo, Sunette Loubser, Yolandi Potgieter, Elriesa Theunissen, Chloe Tryon, Dane van Niekerk.