"We expected to win the T20 series coming into it and we're disappointed to lose it," McCullum said in Wellington after being beaten in the final Twenty20 game by 10 wickets to go down 2-1 in that series.
"I thought we bounced back strongly in the second game," he added in reference to New Zealand's victory by 55 runs in Hamilton. "But I expect us to bounce back strongly in the first of the one-dayers.
"That's a characteristic of this team at the moment. Our ability to bounce back and we are going to have to do so because England will be very confident."
The three-match one-day series against Alastair Cook's team brings added significance to McCullum's side as they look towards the 2015 World Cup that New Zealand will co-host with Australia.
Director of cricket John Buchanan has said the focus for the team over the next two years will be on the one-day game.
Coach Mike Hesson has also explained his selections will reduce over the next few months for their tour of England and the Champions Trophy tournament in June as he forms a squad he expects to take the Kiwis through to 2015.
New Zealand are playing their best cricket in the 50-over format, having beaten South Africa 2-1 in a series last month.
"It's less frenetic. You can play okay in parts of the game but you're not necessarily out of it," McCullum said when asked if the 50-over game was more suited to his team's style.
"In one-day cricket, because it lasts a fraction longer, you are able to fight your way back into the game and I think we have a reasonable game plan especially with our batting and obviously we welcome back Kyle Mills who's an experienced bowler for us in that form of the game."
Mills's accuracy with the ball will be welcomed by New Zealand after they struggled against England in two of the Twenty20s, bowling too straight and full, unlike England's pace attack who banged the ball in hard just back of a length.
England's Twenty20 captain Stuart Broad, who now hands over to one-day and Test skipper Cook, said he felt the quick turnaround would not be a problem for the team, given the arrival of world-class players like Cook and off-spinner Graeme Swann.
"We have not met up as a one-day group yet," Broad said.
"The guys who have had a month or three weeks off will obviously be finding their way back into cricket and it's not easy to do in international cricket.
"It's a pretty tight schedule and it will be important we pick up where we left off (on Friday).
"I think the one-day series is over in six days or a week so there's no time for any slipups and we will have to hit the ground running."
The second match is on Wednesday in Napier with the final game in Auckland on February 23.