Reading were "ready to die on the pitch to get to the FA Cup final", according to Arsenal manager Arsene Wenger.
The Championship side came from behind to take Arsenal to extra-time in the Wembley semi-final and wasted a couple of half-chances to cause a shock.
Only goalkeeper Adam Federici's awful mistake cost them the chance of a penalty shoot-out as Reading lost 2-1.
"They were on a different planet, motivation-wise, to what we had seen on tape," said Wenger.
|Teams to have won FA Cup in successive years|
|1871-72, 1872-73: Wanderers||1889-90, 1890-91: Blackburn Rovers|
|1950-51, 1951-52: Newcastle United||1960-61, 1961-62: Tottenham Hotspur|
|1980-81, 1981-82: Tottenham Hotspur||2001-02, 2002-03: Arsenal|
|2008-09, 2009-10: Chelsea|
"It's the occasion of their lives, they wouldn't give up until the end. We have to congratulate them on their effort."
Alexis Sanchez's double means Arsenal will face either Liverpool or Aston Villa in an all-Premier League final on 30 May.
They also have the chance to become the first side since Chelsea in 2010 and only the 10th in history to retain the trophy.
"When you are in a final you can win, you want to win it," said Wenger, whose side remain second in the Premier League, 10 points behind Chelsea.
"Let's prepare well, finish well in the league, come back here and do everything to win it."