City were truly irresistible at Wembley, dominating from start to finish as they swept Javi Gracia's men aside with consummate ease.
David Silva opened the scoring, Raheem Sterling netted twice, as did Gabriel Jesus, and Kevin De Bruyne got a deserved goal to cap off a sensational performance.
The victory equalled the 116-year long record for the biggest FA Cup final win and rounded off another glorious campaign for Pep Guardiola's men, leaving Kompany with no doubt City are the best.
"It's the best team in the world for me," Kompany told BBC Sport. "To set such a high standard, I'm not talking one year, but two years in a row, it's a privilege.
"The first half was difficult. Second half, as soon as we scored the two goals, they had to come and press, it opened up the game for us and it made it more achievable to make chances.
"It wasn't as easy as the score says, but what a season, what a tremendous club.
"It starts with the manager. We set the standard at the beginning of the season and said we had to go again, go back-to-back [win successive Premier League titles].
"It's the group, a positive group of young players with talent, and of course quality."
City boss Guardiola was also full of praise for his players after they crowned what he called an “incredible” season off with another trophy.
But he told reporters that he wants to see some improvement from the team as they look to win even more silverware next term.
“We have to, always you can improve,” he said. “It was an incredible final for us and we have finished an incredible year.”