The Fijians went down 30-24 to England in their quarter-final at the Velodrome on Sunday, coming up short in their pursuit of a try that would have given them a stunning last-gasp upset.
"I'm a bit speechless at the moment but I couldn't be prouder of the boys," said Raiwalui, who took over the team in February and quickly overhauled the culture.
"They've worked so hard since week one, 15 weeks now, and they've shown they belong on the world stage. The whole group players and staff. It's a bit of an emotional moment.
"This is a different Fiji team and I think it's the start of something special. We made a couple of mistakes today, we didn't take our chances and we paid for it but, as I said, I couldn't be prouder."
Sunday's match had echoes of Fiji's last World Cup quarter-final in 2007 when they fought back to level the match at 20-20 only to go down 37-20 to eventual champions South Africa.
The success of that campaign was not built upon but Raiwalui, who until he took over as coach was general manager at the Fijian Rugby Union, thought this time would be different.
"When I was general manager, the idea was to make sure that pathways were geared towards long-term success. Our pathways are in a good place," he said.
"The second thing was we needed to be more consistent in preparation, and I think what we've shown this year is that we've grown in that area. I think that's only going to grow as we go forward to the 2027 and 2031 World Cups."
It has been a tough few weeks off the pitch for the Fijians with centre Josua Tuisova losing his son to a long-term illness and hooker Sam Matavesi's father dying earlier this week.
Both players stayed in France and Raiwalui said that showed what a special squad it was.
"It's more than just a group, it's a family," he said. "I think we'll have a bond for the rest of our lives."
