Mr Luxon made his comments to media after he and other executives appeared before Parliament's finance and expenditure committee.
The Government owns 53 per cent of Air New Zealand, which is a publicly listed company.
Air New Zealand had a successful year last year, making $474 million profit, before tax. It paid $89 million in dividends to the Government.
Because of its improved performance, the airline also gave all full-time staff who were not on individual bonuses $1400 "in reflection of the improved financial performance of the airline".
New Zealand has seen increased competition in domestic fares, since Jetstar announced last June that it would expand its network to Nelson, Napier, Palmerston North and New Plymouth.
When tickets first went on sale a price war broke out between the two, and regional airfares sold for as low as $9.
Labour's Stuart Nash, MP for Napier, queried why New Zealanders, particularly those in the regions, had not seen prices come down as fuel prices dropped.
"What would you say to people in the regions who say that on the routes where there is no competition, that you engage in monopolistic behaviour?"
Mr Luxon said that was "unfair", and Air New Zealand had valued such communities by running services that connected them.
"Competitors, and we are dealing with a competitor that has four times more resources and scale than Air New Zealand, have cherry-picked the most profitable towns to fly to, but don't service 22 towns across New Zealand.
He said he understood that some people thought prices were high but he said 15 Air New Zealand routes had been losing a total of $1 million a month for three years.
"People may not like the number, but it is airline economics."
Mr Nash said business people in his region had said the biggest barrier to doing business was the price of airfares. He asked whether it was coincidence that Air New Zealand had dropped its prices after Jetstar's entry in the market.
Mr Luxon said Jetstar's low fares could not last.
"A competitor has had very sharp promotional pricing -- 50 per cent service levels at the moment -- that's not going to be sustainable. That competitor is losing a truck load of money."
Mr Nash asked whether Air New Zealand would keep its prices down if Jetstar stopping flying to Napier.
He said his research showed that, on routes with no competition, the fares had not dropped, despite fuel prices going down.
"You can understand the cynicism of people in the Bay, when they are paying $500 return from Auckland, and suddenly there is competition and the price drops. You know, it was like when Telecom was the only game in town."
Mr Luxon said Air New Zealand would react to promotional pricing, and that average fares in regional New Zealand had trended down since 2009.
"I appreciate the perception, but I can tell you we are not sitting there deliberately thinking about how [to] make it tough for regional players in New Zealand to get connected into main centres."
