Wanderers travelled to Al-Hilal on Saturday with a 1-0 aggregate lead from the first leg and made history by claiming the trophy thanks to a 0-0 draw in the return fixture.
Popovic's side had to withstand heavy pressure as the hosts dominated the match in Riyadh, but they clung on for glory in their debut continental campaign, having only been founded in 2012.
Former Crystal Palace defender Popovic described the triumph as a "dream come true" and was quick to pay tribute to the players who had made it possible.
"It's a little tough to sink in at the moment," Popovic told Fox Sports.
"Obviously [I am] very proud of the players. I think it'll sink in once we get out of this stadium.
"[It's a] marvellous achievement from the players, the club, Australian football. We're the champions of Asia - dreams do come true."
Asked if resilience was the word to sum up his team's performance, Popovic said: "You can name so many throughout today and throughout the whole campaign. But that resilience, yup, I'll give you that one for now. But there are so many more I'm sure we'll talk about the next few days.
"It's a special group to coach. They never know when they're beaten. They've made history tonight."
As for where the claiming the AFC crown ranks among his achievements in the dugout, Popovic - who has already guided the Wanderers to the A-League Premiers' Plate and two grand final defeats - was unequivocal.
"It has to rate as the best," he added. "It's been a very short time as a coach, it'll sink in in a few days, but we're just delighted."
The scenes of celebration were tempered slightly by an unsavoury incident in which Al-Hilal's Nasser Al Shamrani appeared to spit at Wanderers' Matthew Spiranovic, following an an attempt to head-butt the substitute late in the action.
That prompted an unseemly melee between players, coaches and officials on both sides at the climax, but nothing could wipe the smile off Popovic's face after his club's historic triumph.
