The Jambos' financial issues have been well-documented, with the club's very future at stake earlier in the campaign.
However, the focus will be firmly on the football this weekend when they battle Inverness for a place in the Scottish League Cup final.
And Webster says Hearts' desire to secure a Hampden return after last season's Scottish Cup triumph is strong irrespective of any off-field factors.
He said: "It doesn't really matter what's going on behind the scenes, it's an opportunity to get to a final and win a cup.
"Everything else gets put to the side.
"When you taste a bit of success with silverware, you're desperate for more.
"It's great to look back and think you have won medals, you've played on the biggest stage, you've given yourself every opportunity to win a trophy.
"Saturday's game is a massive ask for us but we know the incentive is there.
"As a footballer, you want to play in these big occasions and Saturday is a big occasion.
"It's a great incentive to get back to a cup final."
Hearts may be Scottish Cup holders but, according to Webster, winning the League Cup is also an attractive prospect.
He added: "It's an opportunity to win a trophy.
"Nobody is going to go into the competition thinking 'we don't really want to win.'
"When you get that opportunity to win silverware, you are desperate for it."
An impressive run of results mean Inverness are flying high in second position in the Scottish Premier League.
Webster said: "They've done exceptionally well.
"On current form, they're one of the best sides in the league.
"It's going to be a massive task on Saturday but it's one we are definitely relishing."
The defender has not been surprised by Inverness' success so far this season.
He added: "Generally, over the course of the season, a lot of the teams have shown a bit of decent form and a lot of teams have shown a fair bit of consistency.
"There is an opportunity there to do well.
"I've not really been surprised because they do have some quality players.
"I think anybody, if they show a bit of consistency and decent form, can get themselves up there."
Asked if the Highlanders are favourites for the tie, he said: "Probably, yes.
"Saturday is a different kettle of fish.
"They've shown great form, we've shown inconsistency.
"But, come Saturday at 3 o'clock, it will be the best team on the day."
Webster's contract expires at the end of the season but he is not looking to the future just yet.
He said: "The club has probably got enough to worry about for the foreseeable future.
"I'm happy to be here and delighted to be playing so I just take it as it comes."