Villa captain John Terry told Sky Sports: "It's unbelievable and incredible".
"(We've produced) Two very good performances away and at home tonight.
"It was intense. I think our game plan worked very well so the manager deserves a lot credit for that".
The match began with a minute's applause for former Villa defender Jlloyd Samuel who died earlier in the day at the age of 37 in a vehicle accident.
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"It irks me a little bit but the teams who finished third and fourth are going to Wembley and that's justification of what they've done over the season.
It's hard for me to say that but that's being brutally honest".
Villa held on to claim a draw on the night and victory overall, sparking wild celebrations as their fans flooded onto the pitch at fulltime.
And the Villans were content with soaking up pressure from their opponents throughout the match, hitting them on the counter, though neither side could find the breakthrough goal.
He said: 'It's a big club, history and tradition and you need big players.
Fulham advanced after beating Derby 2-0 in their second leg on Monday, sealing a 2-1 win on aggregate. "We're going to Wembley, let's enjoy it".