Ashley Giles believes supporters should be helping to weed out troublesome individuals in the wake of England paceman Jofra Archer being the target of alleged racist abuse during the first Test against New Zealand.

The governing bodies of both teams are investigating after Archer said he heard "racial insults" by "one guy" as he left the field on the final day following his dismissal in England's innings defeat at Mount Maunganui.

As the search for the offender continues, Giles, the managing director of the England men's team, insists spectators can do their bit to stamp out racism by flagging up any issues to security at the ground.

Giles said: "I'm sure someone else must have heard it and I hope they come forward. (If) people are sitting next to this and not reporting it to stewards then there is something seriously going wrong with our society.

"We can't accept that it's just part of society, it happens in lots of sport, we hear about it daily, and we don't need it in cricket.

"I'm sure there is a lot that goes on that isn't reported, unfortunately. There are measures and all sorts of abuse that goes on, I know from my experience, and this is one of those forms that is the worst."

New Zealand Cricket chief executive David White has warned that whoever was responsible faces possible criminal charges and a potential lifelong ban from attending cricket matches in the country.

White apologised to Archer in person on the England team's arrival into Hamilton on Tuesday ahead of the second Test which starts later this week, where security will be beefed up in an attempt to avoid a repeat occurrence.

However, Archer's contact with the perpetrator was seemingly not confined to the field as Giles acknowledged the 24-year-old had been direct messaged on Instagram by the apparent culprit.

Giles said: "I am aware of that, yes.

"It should be quite easy (to find the person) and New Zealand Cricket are into it right now. I'm pretty sure they will find out who it is and come down pretty hard."

Featuring in his first overseas Test, Archer took one for 107 in 42 overs on a docile Bay Oval pitch and was unable to summon the express speeds that made him a breakout star in the World Cup and Ashes over the summer.

England captain Joe Root urged the paceman to "unleash a little bit more" immediately after the heavy loss, which saw the tourists fall 1-0 down in the two-Test series.

However, Giles believes it is unreasonable to expect Archer to be bowling at full tilt all the time and called for him to be nurtured carefully.

Giles said: "We're all different and need different management styles – the carrot and stick will work differently with people. But Jof is gold for us and we have got to look after him. He's really important for our future.

"But we have to be careful how much we think we're going to get out of him every day. And on a pitch that placid, it was pretty hard work.

"We're expecting a hell of a lot from a young bloke, just to run in and bowl 95mph every day. It's not going to happen. Whether that's because he's young and not played a lot of cricket, we've got to help him through that."

Giles had some consoling words for Root, who contributed just 13 runs in two innings against the Black Caps as his batting average as Test captain fell to 39.7, which contrasts sharply with a figure of 52.8 when he is not leading the side.

Giles said: "I think Joe is our captain to take us forward.

"We've got to work with him on his game to make sure his game in the best shape and that he gets time to work on it away from the pressures of captaincy, so that he can get back to averaging 50-plus in Test cricket.

"If he's doing that we are going to win games of Test cricket."

Giles was at pains to throw his weight behind Root leading England into the next Ashes series Down Under in 2021/22, adding: "None of us know what's around the corner but we believe Joe is the man to take us forward."