The hosts are fresh from their emphatic Test victory over the Black Caps, with Cook’s men sealing victory in a rain-affected final day at Headingley.
“It’s very important [to keep the winning habit going],” said Cook at a news conference at Lord’s.
“We’re in a series followed by the Champions Trophy, so we want to win as many games as possible. Winning breeds confidence.”
He added: “It’s one of the challenges of being a player.
“In country cricket, you’ve been brought up playing a four-day game then the next day a one-day game followed by a Twenty20 game.
“We’re all quite used to it but it’s about making sure mentally that we’re right.”
With the ODI series against New Zealand preceding the Champions Trophy, there’s a danger England could be distracted by the tournament which starts on 6 June.
But Cook insisted his side would be focused on beating the Black Caps over the next three matches at Lord’s, the Rose Bowl and Trent Bridge.
“Clearly as players you have to look at it as a series we want to win,” Cook continued.
“Obviously in the long, we’ve got three games and then the Champions Trophy. It’s great preparation for when we get there but we need to look at the series in total isolation.”
Cook also welcomed Kevin Pietersen’s return to the nets as the batsman continues his rehabilitation from a knee injury which caused him to fly home from the third Test of England’s tour of New Zealand in March.
“It’s great news for English cricket to have him back playing again,” added Cook.
“It’s encouraging that he’s progressing well and things are looking positive on that note. Hopefully it won’t be too long before he’s back in the middle.”
Surrey bowler Jade Dernbach has been called up to the ODI squad as cover for Tim Bresnan, whose wife is due to give birth during the series.