Lee, who is one of four goalkeeper at Griffin Park, only started tonight's match because first-choice Ben Hamer was cup-tied.
He joined Brentford on a free transfer from Watford at the start of the season, with an outstanding one-handed save from Mikael Arteta in extra-time the pick of his efforts to keep out a Barclays Premier League opposition packed with internationals.
Boss Scott was quick to lavish praise on the 27-year-old.
He said: "I am pleased for him because he showed how important he is to the club and after a stop start time in his career. I'm delighted for him.
"I said to him before the shoot out 'You have been absolutely outstanding during the match, now go and win it for us' and he did."
Scott was delighted with his side's performance, describing it as the pinnacle of his managerial career.
"It's the biggest win as a game for me as a manager," said Scott. "They have played their fist team and brought on (Stephen) Pienaar, (Mikael) Arteta and (Jermaine) Beckford so we have come up against a very strong side and have beaten them."