The American had not played for the Cottages this season after it became clear he wanted a move, with Liverpool the expected destination.
However, after finally completing a deadline deal to join Spurs believed to be in the region of £6 million, the 29-year-old wants to put the whole saga behind him.
Speaking to Sports Illustrated, Dempsey said: "I just remember calling my wife and my mom and almost wanting to break down in tears because it was a tough time.
"Going into that last day and night there were still a lot of question marks. It wasn't clear-cut this was going to happen.
"Some other things came up and you are going through that struggle, which was not fun for anybody.
"It was difficult for Fulham and for me, not knowing how it's going to end.
"It's just about having that faith, holding onto hope that something was going to happen that both parties were going to be happy with.
"In the end that was accomplished, but the deal didn't get done until right about 9pm, and that was when a fee was agreed.
"But then you had to look at all the logistics, trying to get to Tottenham's training ground, trying to make sure all the paperwork was through, doing the medical, signing the contract and having everything sent back before the deadline at 11.
"Everything was sent through at like 10:58, so you're there, but you're still like: 'Is this official yet?'."
Dempsey denied he had gone on strike to facilitate a move.
He added: "I did not refuse to play. There were some things that were said that were not true."
The American was Fulham's top scorer last season with 23 goals, but is now looking forward to proving himself all over again under Andre Villas-Boas at Spurs.
"It's an opportunity for me to play three more years guaranteed at such a high level and gives you an opportunity to see where you are and if you can make it," Dempsey continued.
"For me, it's always been about being able to look myself in the mirror and say: 'You tried your best. You challenged yourself`. And you'll be able to die a happy man in the sense of your career, knowing that you were able to see if you could do it or not'.
"It is a gamble you take when you make a move to a new team. You don't know where you're going to fit in exactly, you don't know how you're going to gel.
"It will be interesting to see where I will fit in [at Spurs], because I don't know what his plans are in that sense.
"I have to show him [Villas-Boas] where I am at, obviously, and he will see what the best fit will be."
France captain Hugo Lloris was another signed ahead of the deadline, as the goalkeeper joined on an £8million deal from Lyon.
However, Les Bleus coach Didier Deschamps indicated Lloris' position as France number one would be under consideration if he was not able to dislodge American veteran Brad Friedel between the posts at Spurs.
That, though, should not prove an issue, according to Lyon goalkeeping coach Joel Bats.
"He is one of the best three goalkeepers in the world. Hugo could play against any player in any league," Bats said in L'Equipe.
"Now, if he can help Tottenham to the next level, it could be a springboard towards a bigger club."
Lloris played down the issue when it was raised ahead of France's World Cup qualifier against Finland tonight [Friday].
He said: "I am a professional and I can put all this aside.
"I am only and entirely focused on France.
"I have played enough matches in the past to be able to manage this."
Tottenham, meanwhile, could yet allow some more of their fringe players out on loan once the emergency window opens for the npower Football League this weekend.
Midfielder Jermaine Jenas' proposed move to Sunderland fell through, so he could still yet depart if he is prepared to drop down a division for regular first-team football.