Dempsey was one of the standout performer's in Thursday night's 1-1 draw with FC Twente in Europa League Group K.
"Every game is going to be tough, especially away from home," he said.
"You've just got to keep going and I think eventually it will start to fall for us.
"If things keep going the way they are going, we're going to start getting wins.
"No matter who we play we're going to try and get a result.
"We need results now, especially with where we are in the table.
"We're going to go out there, try and do our best to get as many points as we can."
Dempsey believes his team-mates can take encouragement from their creative performance into Sunday's clash against Manchester City.
"The good thing is we're creating chances," he said.
"Eventually they are going to fall for us.
"We did take the lead, going one up. You'd think we would be able to see that out but we weren't able to.
"But we are creating chances so it is just a matter of time until they start falling for us. I'm not too worried."