Nigeria run 'an inspiration for women's football in Africa'
The Nigerians bowed out when they went down 4-2 on penalties to football heavyweights England when their last-16 encounter finished goalless at the end of extra time.
Waldrum said Nigeria, who came into the tournament ranked 40th in the world, had done both their country and the continent of Africa proud.
"They've been fantastic the whole tournament," Waldrum, an American, said.
"I said to them after the game we've not lost a game realistically (outside the penalty shootout).
"We've played against the Olympic gold medallists (Canada), the European champions (England) and we kept a clean sheet in both of those games.
"We played the host nation (Australia) and Ireland, who are in the top 20, and we didn't lose."
Waldrum said Nigeria's performances, alongside those of South Africa and Morocco, should shine a light on African football.
"South Africa was exceptional in their run as well and you saw they created a lot of problems for the Netherlands yesterday," he said.
"I hope what we've done is show the rest of the world that football in Africa is relevant.
"I hope people have seen that there is talent there and that we have the ability, and with a little structure and a little organisation, and a commitment to provide the resources that we need, hopefully people see that we can be a major player on the world stage."
Waldrum said the most important thing was for Nigeria not to lose the momentum they have developed in Australia.
"We don't want to take the success and now not continue to move forward when we get back to Nigeria," he said.
Waldrum said if South Africa were to win the rights to host the next Women's World Cup, it would be a vital step in the sport's growth on the continent.
"I think it would be a great opportunity and it would do wonders for football in Africa," he said.
"For all the nations, for all the young players, to come and see an environment like we have seen in Australia would be massive for all the young women aspiring to play for their countries.
"I hope it happens."
