Crawley stunned the Premier League side with three second-half goals from Nick Tsaroulla, Ashley Nadesan and Jordan Tannicliffe.
Wright came on as a substitute in stoppage time for the League Two club as Marcelo Bielsa's Leeds were dumped out of the cup.
Wright, 33, featured on the famous UK show "The Only Way is Essex" and was a regular for the first three series.
Speaking about his departure from Spurs, Wright told the BBC: "The day I got released from Tottenham, was one of the worst days of my life.
"I cried my eyes out, I realised I messed up. I didn't want to face my family, I didn't want to face my friends. I was embarrassed. I had it all, 18, going to clubs and I just thought, 'It's done.'
"I've been spolied, I played for Arsenal, West Ham and Tottenham all of my life and never had to suffered when it came to football."
Wright has since spent a number of years playing non-league football before League Two club Crawley signed him on a non-contract basis in December.