The England U19 starlet has yet to make his first-team debut for Martin O'Neill's side, but has impressed enough in the past to be included in the Villans' pre-season trip to Switzerland, as well as being named as a substitute for the club's European encounters with Odense and FH Hafnarfjordur.
He is currently on loan at League 2 side Lincoln City, where he has made 11 league outings.
Each member of the Villa squad had been allocated tickets for both family and friends - with strict instructions not to sell them on.
But Baker opted to try and flog his passes for £200 each on social networking website Facebook, with the youngster set to make £1,000 from the sale of all his tickets.
As a result, the teenage talent has now had all of his tickets taken away, and has been banned from attending Villa's first Wembley final since 2000 against the Red Devils.
"The club is saddened that Nathan has been so foolish," a club spokesperson said.
"All of the players were made aware that tickets for the Carling Cup final are available for their own use only and, following this incident, the message has been repeated to them.
"It shouldn't be forgotten, however, that Nathan is just 18 years old and he has a lot to learn. His actions were naive and he is extremely embarrassed and regretful at having let down himself, the club and Aston Villa fans."
And Baker himself has apologised to the Villa supporters for his irresponsible behaviour.
"I wish to apologise unreservedly to the fans for my actions," he said.
"I appreciate it is a privilege to be part of Aston Villa Football Club and one day I hope to play in the first team, but I understand that my behaviour off the pitch must speak as loudly as my actions on the pitch.
"I have been informed by the club that I will no longer be receiving any tickets for the Carling Cup final and, while I will be sorry not to be able to cheer Aston Villa on at Wembley, I understand and appreciate that it would be inappropriate for me to have these tickets given my actions."
Villa are bidding to win their first domestic trophy since 1996 - when they defeated Leeds United in the League Cup final - after eliminating Blackburn Rovers 7-3 on aggregate courtesy of goals from James Milner, Stephen Warnock, Gabriel Agbonlahor, Emile Heskey and Ashley Young.
However, to do so they will have to topple defending champions United, who reached yet another Wembley final after goals from Paul Scholes, Michael Carrick and Wayne Rooney defeated city rivals Manchester City in their semi-final second leg.
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