The midfielder was handed the honour by caretaker manager Stuart Pearce.
In doing so, Scott became just the eighth Spurs player to lead out England and the first since Sol Campbell against the Czech Republic in November, 1998.
He follows some of the club's all-time greats - Vivian Woodward (who captained the side on occasions between 1908-11), Arthur Grimsdell (1921-23), Sir Alf Ramsey (1950-51), Alan Mullery (1971), Martin Peters (1971-74), Gary Lineker (1990-92) and Sol Campbell (1998).
"It was pretty special, really, a very proud moment for me and something, as a kid, I dreamed of many a time," said Scott.
"I could probably speak for every boy and every young lad who has the same ambition.
"I never thought it would happen to me, to be honest, so I'm absolutely delighted to lead out my country.
"It was a very, very proud moment for me to lead out my country."
Scott played the full 90 minutes as England produced a stirring late comeback to recover from 2-0 down to 2-2 - only to lose in injury time.
After a goalless first half, Arjen Robben and Klaas Jan Huntelaar put the Dutch 2-0 up, but Gary Cahill and ASshley Young struck in the final five minutes to make it 2-2.
However, in the game's final attack, Robben's curler deflected off Cahill to leave Joe Hart with no chance.
"I thought we showed great heart, great courage to get back into the game," added Scott, who won his 11th cap.
"At 2-0, we could have fallen apart, really. We dug in and we got ourselves back.
"It's probably a little sloppy on our behalf that we've let them go and win the game.
"It's disappointing but we got some good positives out of the game."