The former France striker earned his side a point with an injury-time penalty in the Group A clash, cancelling out Michu's 68th-minute strike at the Liberty Stadium.
However, he insists that he did not feel any pressure in the build-up to the spot kick, despite how much was riding on it.
"It'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 the pressure, I just had to put the ball in the net.
"We don't have big names in the team but we played some really good football. We showed that tonight. We are going to back home with one point and we are not going to do a five-hour flight for nothing."
Despite the dramatic draw, Kuban sit bottom of the group and the former Liverpool striker called upon his team-mates to boost their chances of making the last 32 with a win in the return fixture in two weeks' time.
"They are going to have a really difficult game when they come to Russia," he continued.
"We are back in the game and we know if we manage to win at home, we are still in the race for qualification."