Spurs will head into the Premier League clash off the back of a defeat to Chelsea last weekend and a draw with Maribor in the Europa League on Thursday.
"It's always difficult on the road in the Premier League and it will be on Sunday because Southampton are clearly a good team that have shown that they can score goals," he is quoted as saying by the Daily Mail.
"After playing on a Thursday night on the other side of Europe you just have to make sure your body is right and that you are taking care of yourself in the way you need to.
"All you can control is how well you rest, rehab, take ice baths and train. You must stay sharp and be able to give your best effort. It's a busy schedule but every team has to deal with it. We'll just have to keep plugging away."
Dempsey further underlined the importance of winning on Sunday and keeping themselves among the top five in the Premier League.
"What's important is that we bounce back from the loss to Chelsea," said the 29-year-old.
"Before Chelsea we were on a good run of form and hadn't lost in seven games. We've been good on the road and it's vital we get as many points as we can to keep ourselves in the top five."
Spurs are currently seventh in the league with 14 points from eight matches.