Remarkably, Spurs had three goals ruled out at White Hart Lane and had to settle for a goalless draw against Vladimir Petkovic's Biancocelesti.
He told ITV: "I thought I was level with the line, it was a good ball from (Gareth) Bale and as it went in I thought I'd opened my account but it was waved offside.
"That's the way it goes sometimes, they defended well, set up to counter-attack and were tough to break down.
"But we had some chances and were unlucky not to get the goal tonight [Thursday]."
Dempsey was a deadline-day capture from Tottenham's cross-city rivals Fulham, and despite being denied the chance to register a first goal, the American is pleased with the way things are going.
"It's good to be getting games," he added.
"I'm trying to create chances or trying to get on the end of things, I can play in other positions.
"They were tough to break down, they set out to defend and played for the counter.
"We had some good chances and were unlucky not to get a goal."
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Defender Steven Caulker also had his goal ruled out for a perceived push on his marker.
He added: "I thought it was a little harsh but I haven't seen the replay yet.
"I'm glad to keep a clean sheet and I think we'll go forward in the next game.
"They're one of the stronger sides in the group so we're pleased with the point.
"We set out to win but we'll rebuild and go again."
Meanwhile, Spurs manager Andre Villas-Boas is sure that UEFA will come down hard on any Lazio fans who are found to have racially abused Tottenham's players during the game.
Loud monkey-chanting was heard to come from the away end on several occasions directed against Jermain Defoe, Aaron Lennon and Andros Townsend in the Group J clash.
Villas-Boas said he did not hear the chants himself, but he would encourage UEFA, whose head Michel Platini was at the game, to take any action if it is proven that the travelling fans did in fact hurl racist abuse.
"I think (UEFA will act if the accusations are proven)," Villas-Boas said in his post-match press conference.
"UEFA is very active on this kind of situation so and our overall objective is to kick racism out of football.
"I can't point the finger at anyone in any way shape or form tonight [Thursday] because I didn't hear anything. It's for the authorities to follow up in any kind of investigation."
Villas-Boas felt his side did enough to beat Lazio and declared himself happy with their considerable efforts.
"I think we did enough to get the win today [Thursday]," he told ITV4. "I am extremely happy with the performance and the effort that the players put in.
"You can't reprimand them for anything, they were outstanding.
"They managed to create enough opportunities to win the game.
"The team put the ball in the back of the net three times, but all the goals were disallowed by the ref, so it's a bit disappointing.
"It shows that we are on the right track to giving something back to the fans.
"We were superior against a team that is doing extremely well. We can be happy with that performance."
Caulker, who has developed his skills during loan spells at Bristol City and Swansea, was trusted with the responsibility of marshalling the Spurs backline.
Youngsters Andros Townsend and Ryan Mason also acquitted themselves well against the likes of Miroslav Klose, Hernanes and Stefano Mauri.
And Villas-Boas is pleased to see a new generation coming to the fore, adding: "This club has always promoted young talent.
"We managed to give Andros a couple more minutes today [Thursday], Caulker was outstanding at centre-half against one of the best strikers in the world.
"These players have been taught well in their education and it was great to see them."