The north London club suffered a 4-2 home defeat by Chelsea in their last Premier League outing and followed that with a 1-1 Europa League draw in Slovenia against Maribor in midweek and the midfielder is looking for a swift response.
"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," Dempsey told the Daily Mail.
|7/1||Clint Dempsey is 7/1 with William Hill to score two or more goals against Southampton
"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."
Spurs were widely expected to progress from their Europa League group when the draw was made and Dempsey believes that they can still achieve that despite an unconvincing performance against Maribor.
"At least we ground out a result," he observed. "We showed character to get back in the game and put ourselves in a position where we are still right there in the group. The group remains very tight and there is everything to play for.
"We're taking every competition seriously, including Europe. We want to do well in everything."