The Lilywhites' campaign hangs in the balance following their midweek Champions League exit at the hands of the Italian heavyweights at Wembley Stadium.
Speaking after the match on Wednesday night, Chiellini claimed that Tottenham "always miss something at the end" as it is 'part of their history'.
Spurs centre-back Vertonghen is adamant that his teammates have it in them to end the club's decade-long wait for a trophy, though, beginning with success in this season's FA Cup.
"Whenever I won my first trophy, it was just: 'We want more.' It took me six years, maybe five years, to get my first trophy with Ajax, but it feels like you have to win a trophy to win more and then they follow," he is quoted as saying by the Daily Mail.
"It's just the belief you can win it. We've got the right mentality and I know we have what it takes to get there. Hopefully we will get another chance to show that to the world. So, hopefully we can win the FA Cup this year and the rest will follow.
"We've got two things to focus on - the top four and the FA Cup - they're the two main goals this season. This team can reach a lot and it's always nicer to have achieved this with a group of players who have been together for a lot of time and came through the ranks or have lived in London for a long time.
"To do that with this group of colleagues and friends, that's a better feeling than just going somewhere and winning a trophy. It will give us a lot if we win something with this group. I can't speak for others but I believe that they believe we will get that here - that trophy - and they will stay here."
Before facing Swansea City in the quarter-finals of the FA Cup, Tottenham first turn attention to Bournemouth in the Premier League on Sunday afternoon.