"This research exposes the despicable actions of a small number of perpetrators who are sexually abusing some of the most vulnerable children in the world, the very children they are meant to protect."
The UN secretary-general described the report as "very serious" on Tuesday.
Ban Ki-moon said: "I think the report is very valuable and it does give us some good points that the United Nations should continue to address.
"This sexual exploitation of minors by any aid workers or peacekeepers ... that is a very serious issue.
"I have made it always clear that my policy on this sexual exploitation abuse is zero tolerance, we will address this issue with the same level of emphasis.
"However, on all these cases which have been raised, we will very carefully investigate and whenever there is necessary matters, we will take necessary measures on this."
The charity said "endemic failures" in responding to official reports of the abuse were letting down the victims and that better reporting mechanisms should be introduced.
Whitbread said that the UN as well as humanitarian and aid agencies have made important commitments to tackling the problem in recent years.
But she said most had failed to turn their promises into action.
She called for all agencies working in emergency areas, including her own charity to "own up to the fact that they are vulnerable to this problem and tackle it head on".
The UN Department for Peacekeeping Operations (UNPKO) was said to be the group most likely to be responsible for abuse.
Save the Children said there had been 15 claims against UNPKO staff and partners last year, of which three were upheld.
Nick Birnback, a UNPKO spokesman, said it was "entirely unacceptable" that those sent to help the most vulnerable are instead causing grievous harm.
"Clearly a lot more has to be done," he told BBC radio but he rejected allegations that the problem was widespread and those responsible were getting away with it.
"The vast majority of UN peacekeepers all over the world, of which we have over 100,000 now, serve with honour and courage in very difficult situations and don't engage in this unacceptable behaviour," he said.
The reputation of UN peacekeepers has been tarnished in the past by cases of sexual abuse against women, notably in the Democratic Republic of Congo (DRC), Ivory Coast and Haiti.
In November last year, the UN said that more than 100 Sri Lankan soldiers were to be sent home over charges that they paid for sex while stationed in Haiti.
In 2005, the world body recommended that the soldiers involved be punished, their salaries frozen and a fund set up to help any women or girls made pregnant.
The UN's "zero tolerance" policy towards sexual misconduct includes a "non-fraternisation" rule barring them from sex with locals.
It was brought in after revelations in December 2004 that peacekeepers in the DRC were involved in the sexual abuse of 13-year-old girls in exchange for eggs, milk or cash sums of one dollar.