Jurgen Klinsmann's side fell to a 1-0 defeat in Recife after Thomas Muller's second-half strike, but qualified for the knockout stages due to a superior goal difference compared to that of Portugal.
However, speaking to Goal after the game, Dempsey was adamant the United States had earned the right to stay in the tournament and spoke of the need to re-focus ahead of their last-16 clash.
"We're not happy with the result in terms of losing the game," the 31-year-old said.
"But I think we deserve to go through to the next round and we're excited about the possibility of getting to the knockout stages, which is what we always wanted to do. The fact that we were able to get out of a very difficult group shows the belief that we have in ourselves.
"Everything is fresh again. It doesn't matter what you did to get out of the group stages, it's about what you're going to do on that day.
"You know in the back of your mind that a draw gets you through. It's not like a normal game because there are a lot of factors that play into it."
Recife was hit by torrential rain on Thursday, which left roads flooded ahead of the United States' clash with Germany, and Dempsey admitted that the consequences of the unusual conditions had an affect on his concentration during the match.
"It was weird conditions because of the rain and not having a proper warm-up," the Seattle Sounders midfielder added.
"On the field you're having to go behind the goal, not being able to do a possession game and not being able to get shots on goal. It was just a weird preparation.
"And also in the back of your mind you think about your family not being able to make it to the game because of the traffic and everything, and you just want to make sure they're safe. There were just a lot of factors going into today's game that made it a difficult one for both teams."