New Zealand Football asked for intervention from the highest levels of the Peruvian government - including the Ministry of Defence - after the military jet flyover above the team hotel.
NZF sent messages to Wellington just after the incident on Wednesday (local time), which were then conveyed to their Peruvian counterparts.
The New Zealand Herald understands that the Peruvian Ministry of Defence was contacted, ostensibly to ask how the flights had been sanctioned and also to ensure there would be no further episode.
New Zealand's ambassador to Peru, who was in camp with the team, also laid official complaints through government channels here.
The All Whites had put up with a series of disruptions since arriving in South America, starting with their charter plane's arrival in Lima being delayed by almost three hours, after the Peruvian airport authorities cancelled their original flight plan.
There were all kinds of other issues - culminating in fireworks outside the team hotel at 2.45am and 3.45am on match day morning - which had been expected and anticipated, to a degree.
But the jet flyover in the early afternoon, which was at remarkably low levels, not far above the All Whites squad located on the 15th and 16th floor of the Marriott hotel, was seen as a step too far.
There was concern about how the flights had been sanctioned, with approval needed from military and government officials. It also appeared to have been planned well in advance, as the gliders, para-ponting and para-sailing that were a common sight every day above the ocean next to the team hotel were strangely absent.
It was deemed a show of unnecessary aggression, and there was also concern for the small group of New Zealand fans who were spread across the city.
"The fact that it was clearly a sanctioned action, that is clearly a step too far," said NZF chief executive Andy Martin. "We expected some disruptions and hassles here - that's how it is - but when the military get involved that is another level."
"It wasn't just the team, it was the rest of the Kiwis that were here. It was worrying. If that sort of involvement had taken place - which clearly had to be sanctioned for those sort of planes to fly - we wanted to make sure we had assurances for the safety of all of the Kiwis here, and in particular getting to the ground."
"We were in the advanced group going to the ground last night and it was pretty difficult getting through," added Martin. "The police escorted the team through later on. We were protected, to a degree, but there were Kiwis fans out there just walking to the ground and we wanted to make sure they were going to be okay."
Peru won the match 2-0, ending the All Whites' dream of making the World Cup.
- By Michael Burgess in Lima
