As a player, Di Matteo scored after just 42 seconds of the 1997 FA Cup final to help the Blues lift their first trophy since 1971.
Chelsea went on to win the Cup Winners' Cup, the League Cup and the FA Cup again over the next three years before Roman Abramovich's arrival took the club to the next level.
But after three league titles in five years, Chelsea finished trophyless last season and they are already 11 points adrift of leaders Manchester City this term.
Di Matteo believes the FA Cup is Chelsea's best chance of silverware this year - and of reigniting success at Stamford Bridge.
"That goal made a difference to my career and for the club's future because it meant we were playing in Europe the season after and we won the Cup Winners' Cup," Di Matteo said.
"It was an important moment because we were looking to improve and win our first trophy in 27 years. It started a successful cycle in the club.
"(Not winning a trophy) has happened to many other big clubs. But these players have been very successful in their careers in past years.
"Maybe this (the FA Cup) can reignite a new cycle. Trophies bring belief and confidence you can go on to win other things."
Abramovich has shown little patience for managers who have failed to deliver trophies and Di Matteo is acutely aware of the pressure on Chelsea to succeed.
"We are Chelsea, we are expected to win and we want to win," said Di Matteo.
Chelsea open their FA Cup campaign against Portsmouth without Didier Drogba and Salomon Kalou, who are both on African Nations Cup duty, while there are injury concerns over John Terry.
There will once again be a youthful look to the Chelsea bench, but Di Matteo stressed they would be fielding their strongest available team.
"The FA Cup is always a trophy you have the ambition to win and get back into this club," Di Matteo said.
"It is valued highly. The whole country gets excited about this competition and it still holds the same value in the minds of people and players alike.
"This club have been very successful in the competition in the last decade."
Di Matteo's goal against Middlesbrough was the quickest in FA Cup final history, a record since broken by Louis Saha against Chelsea in 2009.
The Italian's long-range strike dipped over goalkeeper Ben Roberts and brushed the underside of the crossbar - and Di Matteo knew it was in from the moment he struck it.
"I more or less knew it was because I could see the path of the ball," he reflected.
After a stint in management with West Brom, where he worked with Portsmouth boss Michael Appleton, Di Matteo is enjoying his time coaching under Andre Villas-Boas.
"When we are working we are deadly serious but he is a great guy, a funny guy," Di Matteo said.
"I love this job. I love what I do. I have ambition and drive to get up every morning."
