Alastair Cook still believes England can regain the Ashes this summer but he has told the struggling batsmen Ian Bell and Gary Ballance they must go away and put their games in order before the first Test against Australia in Cardiff on 8 July.

Speaking after the 199-run defeat by New Zealand that left the two-Test series drawn 1-1 – and on a day when Bell, Ballance, Jimmy Anderson and Stuart Broad were all dropped for the one-dayers – the captain was in defiant mood.

Asked whether he still thought beating Australia was possible, despite England winning only one Test series in their last five, Cook said: “Yes, I do. I think in our conditions as well we are comfortable. But we have to make that step forward as a side and we have to do it quickly.”

The early-season encounter with New Zealand has highlighted a worrying dip in returns from Bell and Ballance, with the former averaging 6.28 in his past four Tests and the latter’s technique facing scrutiny during a run of six innings without passing 30.

With both batsmen among six players from the World Cup to be left out of the 50-over squad, Cook believes that, as with his own resurgence since being dropped from that tournament, the pair can use the additional time to seek remedial help before having to face bowlers such as Mitchell Johnson and Mitchell Starc when they play Australia.

“Clearly they haven’t scored the runs – that is the black and white of it,” said Cook, who was named man of the series for England after scoring 309 runs in four innings. “They have five weeks to go away and find form. They are fantastic players and both their records suggests that.

“They will be concerned because they haven’t scored the runs but it wasn’t long ago I was struggling and form comes and goes. They have a lot of hard work to do but two games in isolation don’t make you a bad player.”

The breakneck speed of New Zealand’s cricket, in which they scored at 4.92 runs per over at Headingley before bowling England out for 255 on the fifth day, has only highlighted the disappointment that there will be no decider between the two sides – something Cook agrees with.

“I get blamed for a lot of things but you can’t blame me for the schedules,” he said, jokingly. “Both sides would have loved another Test match. One-all feels like there should have been more. If you were a boxing promoter you’d want a rematch now, wouldn’t you? Both sides played it as cricket should be played and the standard has been high.”

One area where the standard dropped, however, was England’s catching, with nine chances going to grass during the course of the series. Cook admitted there were areas to work on but he had seen plenty both at Lord’s and in Leeds to remain optimistic.

“We let things slip but there are positives,” he said. “It was great for Adam Lyth to get a hundred on his home ground – that is the stuff dreams are made of. Ben Stokes did well, not only at Lord’s, but in a tough situation at Headingley and Mark Wood has added fire to our bowling line-up.”

Cook’s opposite number, Brendon McCullum, who guided his side to the World Cup final in March, said that leading New Zealand to only their fifth Test win on English soil will rank among his greatest achievements when he retires. He knows cricket will always come second in his country to rugby but the 33-year-old hopes a new generation will be inspired.

“England is a tough place to tour,” McCullum said. “There is the ball and the conditions, plus England are a very good cricket team in their own backyard. We will look back in years to come and be very proud.”

He added: “We’ll never get near rugby – it’s in our blood. From when you are born in New Zealand you try to become an All Black. But we were able to captivate our nation during the World Cup and performances like this will help. If it sees one or two extra talents coming through to choose to play our sport, then that’s great for the game.”