Webster won the Scottish Cup with Dundee United in 2010 before repeating the feat with Hearts last year and will lead the Edinburgh side out against St Mirren on Sunday in the absence of injured captain Marius Zaliukas.
The 30-year-old, who was at Hampden to promote the final, said: "Once you have finished your career you can look back and sit down and look at what has been and what could have been.
"But it's like anything, the more you experience it the more you want it, and Sunday is another opportunity for us to win.
"We had a great experience here last year with the Scottish Cup so it's something we will be looking to replicate on Sunday.
"Hopefully it stands you in good stead. There is a bit of experience.
"A few of us have been here before and know what to expect so hopefully that experience comes through on Sunday."
Webster's cup success came after some frustrating times earlier in his career.
The Scotland defender missed Hearts' 2006 Scottish Cup final win after being sidelined by club owner Vladimir Romanov when he declined a new contract offer.
A protracted move to Rangers followed and Webster would no doubt have anticipated the chance to win silverware.
But the centre-back made only three first-team appearances in light blue, only to find success at Tannadice and Tynecastle.
"You take these things as they come," Webster said. "I always have to look at it in a positive manner.
"It's great to win football trophies and this is another opportunity."
While Hearts have won three Scottish Cups in the last 15 years, League Cup success has eluded them since 1963.
Webster said: "It's been 50 years and you look at some of the Hearts sides of the past. So it's a great opportunity for us to make a little bit of history."