Saints will be the first team to face post-Mourinho Spurs when they travel to north London. The match comes hot on the heels of Southampton's defeat by Leicester in Sunday's FA Cup semi-final, and four days before Tottenham face Manchester City in the Carabao Cup final.
Hasenhuttl said: "We don't have a long time to prepare for the game, and it makes it even more difficult now. It's even more difficult because at the weekend they have a big final, but we have to handle it and concentrate on us.
"It changes everything. Because everything you normally tell your players, what they have to expect, from one day to the next, is not there anymore.
"We have a few hours to concentrate for this and we will try to find a team which is fit enough to compete against them."