Morgan has a new-look squad to face the Kiwis as England look to bounce back from a dismal World Cup.
The five-match series begins at Edgbaston on Tuesday.
"For a long time now, we've been behind the eight-ball in one-day cricket and fallen behind by a long way," said Morgan. "It's time for a catch-up."
Morgan, 28, took over the one-day captaincy from Alastair Cook in December, two months before the start of the World Cup.
England went on to exit the competition at the group stages, losing to minnows Bangladesh along the way.
Now, as they attempt to rebuild, England have left out a number of established players for the series against New Zealand.
James Anderson, Stuart Broad, Ian Bell, Gary Ballance, Moeen Ali, Ravi Bopara and James Tredwell are all missing.
Instead, James Taylor, Alex Hales, Jason Roy, Adil Rashid, David Willey, Mark Wood and uncapped wicketkeeper-batsman Sam Billings will get a chance to shine.
"I've got the squad that I've wanted," said Morgan.
"The guys we have brought in do something different and we want that to continue.
"If they play as well as they have done in county cricket, things will be very exciting."
New Zealand have already secured a draw in a two-match Test series against England this summer.
The Kiwis excelled at the World Cup, losing in the final to Australia, having thrashed England by eight wickets along the way.
"I think it's an exciting squad England have picked," said Black Caps skipper Brendon McCullum.
"It's obviously a little bit raw, but it's full of talented players and guys who are pretty aggressive with both bat and ball."
England (from): Eoin Morgan (capt), Sam Billings, Jos Buttler (wkt) Steven Finn, Alex Hales, Chris Jordan, Liam Plunkett, Adil Rashid, Joe Root, Jason Roy, Ben Stokes, James Taylor, David Willey, Mark Wood
New Zealand (from): Brendon McCullum (capt), Corey Anderson, Trent Boult, Grant Elliott, Martin Guptill, Matt Henry, Tom Latham, Mitchell McClenaghan, Nathan McCullum, Luke Ronchi (wkt), Mutchell Santner, Tim Southee, Ross Taylor, Kane Williamson, Ben Wheeler
Umpires: Bruce Oxenford (Aus), Michael Gough (Eng)
TV umpire: Steve Davis (Aus)
Match referee: Javagal Srinath (Ind)
England one-day captain Eoin Morgan says his side will begin their ODI series against New Zealand having lost ground on the world's leading teams.