The 33-year-old has also won two League Cups and an FA Cup, and knows that talking a good game will not be enough to win Spurs a first trophy since 2008.
"We are moving in the right direction," said Hart. "Jose [Mourinho] inherited a good team and he has made some shrewd additions.
"There is a big difference between saying you want to win something and showing and believing and doing the right things to put yourself in the best position to win.
"Where you want to be is when all the finals are over and the Premier League is finished, everyone can look at each other and say we left nothing out there and threw everything at it."
Hart joined Spurs on a two-year deal in August after his contract expired at Burnley and he has quickly established himself ahead of Paulo Gazzaniga as understudy to club captain Hugo Lloris.
The former England No1 had been expected to find a club where he could be first choice but says he joined Spurs because he loves the environment of being at a big club.
"I crave football," Hart said in an interview with BBC Sport. "I realised I just love being at the top. I love being around a club where you play three games a week and if you don't win it is a big deal.
"I am not stupid. That opportunity was not going to come in a given number one slot. After working out what Jose wanted from his squad and what he thought I could bring to it, it matched what I thought. I haven't come to shake it up. I have come to make Tottenham better."
Spurs manager Jose Mourinho is expected to make a raft of changes for the match in Belgium – which will be played behind closed doors after Belgium reinstated the ban on supporters at the weekend – with Gareth Bale to start, and Carlos Vinicius, Giovani Lo Celso and Serge Aurier also in contention.
Harry Kane is expected to be rested, having already been directly involved in 13 goals in just six League matches this season.
Hart, who was part of the England squad when Kane was first called up in 2015, believes his new Spurs team-mate is "virtually faultless" as a player.
"He has always had that ability," said Hart.
"I struggle to find a fault with Harry. He is absolutely brilliant. Every single pass, every single shot, every single decision.
"He is such a team player. His leadership is doing it, which is often more important than being vocal.
"We have seen how selfless he is. He is a special player and I love being in the same team as him."
Mourinho has left Eric Dier, Tanguy Ndombele and Japhet Tanganga in London, while Paulo Gazzaniga, Gedson Fernandes, Joe Rodon and Danny Rose are ineligible in the Europa League.
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