A 37th minute Thiago Cionek own goal and a 60th minute strike from Mbaye Niang ensured three points for the Teranga Lions in the Group H fixture at Otkritie Arena in Moscow.
Grzegorz Krychowiak pulled one back for the Red and Whites four minutes to full-time.
"Senegal won thanks to its discipline, we were compact [and] aggressive," Cisse said after the game.
"We were very good in the offensive and defensive transitions in the first half.
"They had more possession, but as soon as they made a mistake, they were beaten and kicked back.
"We knew they were a very good team technically.
"We had to close them down so they don't gain confidence. That's what we did."
Senegal's triumph was hailed across Africa, considering the poor run so far of the other representatives of the continent at the showpiece.
And after the Poland victory, there was yet another defeat for Africa as Egypt fell 3-1 to the hosts in their second fixture.
"Senegal represents the entire African continent," Cisse remarked.
"The whole continent is behind us. I get calls from everywhere. People believe in us, it's a pride to represent Africa.
"Winning the first match puts you in the right mood. The second game is important, the third too.
"I hope that Egypt, Morocco, Tunisia and Nigeria will recover."