Cisse earned his side a draw with an injury-time penalty in the Group A fixture, cancelling out Michu's 68th-minute strike at the Liberty Stadium.
The Russian Premier League outfit played well during the match and were well worth their point, with Cisse insisting he did not feel the pressure before scoring the spot-kick.
"(To take an injury-time penalty) … that's a delight for strikers. Sometimes you have one chance and you have to score," Cisse told ITV.
"Even if it is in the 95th minute, you have to score. That's your job. I didn't feel no pressure. I just had to put the ball in the net.
"We don't have big names in the team but we play some really good football. We showed that tonight.
"We are going to back home with at least one point and we are not going to do a five-hour flight with nothing."
The former Liverpool and QPR striker believes the result has kept Kuban's hopes of progressing from the group stage alive.
Kuban have won just one point from their three matches, with Cisse's goal the only one they have scored.
But with a home fixture against Swansea to come next month, the French forward is confident.
"They are going to have a really difficult game in our field," Cisse said.
"Now we are back in the game and we know if we manage to win at home, we are still in the race for qualification. It is going to be really tough for them (Swansea)."
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