Kasperczak's men headed into their final Group B match against Zimbabwe knowing a draw would be enough to eliminate Algeria, which was faced with a much-changed Senegal in Franceville.
Naim Sliti hit a ninth-minute opener at the Stade d'Angondje and Tunisia had three more before half-time as it romped to a 4-2 win, securing a meeting with Burkina Faso at the same ground on Sunday (AEDT).
"We came to play without speculating, without calculating," Kasperczak said. "We went out to win; we did not want to control and have a draw.
"I think Zimbabwe were surprised by the way we were playing - kind of aggressive with our presence.
"Fortunately we had efficiency that caused us to score goals. I do not think we have to change the strategy in order to go further in the competition.
"As we have seen until today, the matches are played on details. Fortunately in the first half we made a difference and in the second half our players were able to control the game.
"Burkina Faso and Tunisia deserve their qualification for the next stage and we hope to be able to make it to the semis."