The 29-year-old, who has been at Spurs for seven-and-a-half seasons, was injured when his teammates beat Chelsea in the 2008 League Cup final.
He has since played at Wembley on three occasions for Tottenham, losing in the semi-finals of the FA Cup in 2010 and 2012 to Portsmouth and Chelsea respectively, and to Manchester United in the 2009 League Cup final.
"We spoke to the gaffer at the start of the season and we said we want to win trophies, as players and as a team," Dawson told Spurs TV Online.
"That's what you look back on at the end of your career. We have had two Wembley trips in the League Cup - one win and one loss.
"Wembley is a special place. To go up those steps and lift that cup would be special. And every player will say the same as me - the FA Cup is massive for us."
Dawson's current contract is due to expire in June 2015.