The American had not played for the Cottagers this season after it became clear he wanted a move, with Liverpool the expected destination.
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."
He added: "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."