The North Africans were beaten 2-1 by Croatia in the third-place play-off at Khalifa International Stadium on Saturday night.
However, the second straight defeat – Morocco were unbeaten in their opening five matches at the tournament – should not take away from what has been a remarkable achievement overall.
Morocco became the first Arab nation to reach the World Cup quarter-finals, and sit as the only African side in history to reach the last four.
Speaking directly following the Croatia loss, Regragui said: “We had 0.01 per cent of winning this World Cup at the outset. We managed to get through to the last four. We played against some of the footballing powerhouses of the world.
“We're now one of the top four teams in the world and if you had told me that before the World Cup and that Morocco would be No 4 in the world, I would have accepted that straight away.”
Against Croatia, Morocco were without a number of key players, including captain Romain Saiss, defensive partner Nayef Aguerd, and Bayern Munich left-back Noussair Mazraoui. Meanwhile, impressive midfielder Azzedine Ounahi began on the bench.
The quartet was instrumental in Morocco finishing top of a group that contained Croatia and Belgium, before then defeating Spain, the 2010 champions, in the last 16 – the country’s first World Cup knockout match in 36 years.
"Sure, I am a little disappointed by this second consecutive defeat, but we did everything that we could," Regragui said. "Physically it was difficult; our players got tired. It was very intense.
“We wanted to make the fans more proud than they already were, that's it. We wanted to bring joy to them, but we're still happy: we're among the four best teams in the world.
"We provided everyone with a good show. We never gave up. Congratulations to Croatia, they deserve their third place. We are a young team that is still learning.
“Of course, we're disappointed, but when we wake up tomorrow we will realise how much we have achieved… some of my players weren’t 100 per cent fit but they gave everything to the end. I am very proud.”
Croatia v Morocco player ratings
Despite the defeat, Morocco are viewed as a major success story, and enjoyed the support of the African and Arab world throughout their run in Qatar.
"I think we showed our strength, we showed that African football is prepared to face the top teams in the world with efficiency and playing at the highest level," Regragui said.
"We probably will only realise what we accomplished in Qatar after four years, in the next World Cup. The pressure will also be greater, there will be expectation around us. It's natural.
"We made a great achievement, but we want to do it again. It will not be easy but that's the objective."
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Regragui, who was appointed only in August, said he hopes his side would leave a lasting legacy for African football.
"Through experience you get stronger and I hope we learn and grow and build in our children in Africa a football DNA that lasts," the former Morocco international said.
"We have now allowed children to dream, dream of being footballers and going to the World Cup. That is priceless. As for the impact in our country, we have set the bar high.
"I'm sure that in 15 years an African team will win the World Cup."