Steve Bruce's side were much improved in the second period, with Grealish heading over from close-range.
He is a likely departee, while Villa's star attraction, 22-year-old midfielder Jack Grealish, is likely to be a target for Premier League clubs in the summer. "For me, Fredericks should have had a red card", he said.
Saturday may be the day of the Champions League final but the financial implications of the second-tier showpiece - worth at least £160 million of additional revenue to the victor - dwarfs the Kiev showpiece.
The win, which sees the Cottagers return to the Premier League for the first time since the 2014/15 season, capped off what was an unbelievable turnaround for Slaviša Jokanović's side.
"I don't know (whether I will still be at Fulham next season)". We just needed a break, but we didn't get one.More news: How the Weinstein allegations led to criminal charges
Teenager Ryan Sessegnon received the ball midway inside Villa's half, evaded a tackle, and turned to play a through ball that Cairney calmly slotted past keeper Sam Johnstone.
All three of the clubs promoted in 2017 survived relegation this past season for only the third time in Premier League history.
However, the report also suggests that Wolves are in the hunting for the forward and, considering their track-record of attracting Porto stars in the past, the Villains must act quickly if they are to grab themselves an assured European goalscorer.
Despite only Matej Vydra (21) scoring more goals in the Championship this season than Lewis Grabban (20), the Villa striker's poor luck in the play-offs continued on Saturday.
"We were disappointed with the first half", Bruce said.
It was an unforgettable evening for Fulham, who were making their first appearance at Wembley since losing the 1975 FA Cup final against West Ham.
"I believed in the way we play, and the manager has put a lot of faith in me. I'm happy with what my team offered today and how we played our football".