Cisse conceded there was an element of luck as Senegal benefited from a deflected Thiago Cionek own goal and a terrible error by 'keeper Wojciech Szczesny, but said the Polish mistakes came through pressure exerted by his team.
"We earned out victory, we worked very hard for it," he said after the win, which puts Senegal at the top of Group H, ahead of Japan on goal difference.
West Bromwich Albion midfielder Grzegorz Krychowiak got Poland back in the game with an 86th-minute header but Senegal held on at Moscow's Spartak Stadium.
It was a match billed as a straight fight between super-strikers Robert Lewandowski and Sadio Mane but Cisse said Senegal "controlled the game tactically and emotionally" to contain the Bayern Munich dangerman.
He said they would bring the same focus to their next match against Japan on Sunday, when Poland will play Colombia.
"Let's not underestimate Senegal. We knew this Poland team very well," he said.
"We knew their systems... we knew exactly how this team was going to move and that Lewandowski was their main threat, and we implemented the right system to play them."
Poland coach Adam Nawalka was fuming at the performance of his team, ranked eighth in the world to Senegal's 27th.
"There were many bad elements in the match," he said.
"We did not match our opponent's quality. The Polish team will have to regenerate and recuperate."
Poland are in the finals for the first time since exiting at the group stages in 2006 and are desperate to improve on the third-place finishes in 1974 and 1982.
Senegal's only previous appearance was in 2002, when they made the quarter finals after a run that included a famous win over defending champions France in the tournament's opening match.
Cisse said the whole of Africa was closely monitoring the progress of Senegal.
"Senegal today represents the whole of the African continent," he said.
"Of course we represent our country but I can also guarantee that the whole of Africa is supporting us. I'm getting phone calls from everywhere."
Liverpool striker Mane set up Idrissa Gueye in the 37th minute for a shot that took a wicked deflection off Cionek, leaving Szczesny totally wrong-footed in the Polish goal for Senegal's opener on 37 minutes.
The lead doubled on the 60-minute mark thanks to Szczesny's howler. Krychowiak put Poland in trouble with a woeful bouncing back pass and the 'keeper rashly opted to charge out of his penalty area to try to clear the danger.
Instead, the speedy Mbaye Niang got in front of his defender, nicked the ball away from Szczesny and rolled it into the empty net.
It was the always-dangerous Niang who was at the heart of Senegal's opening goal.
The Torino winger won the ball on the halfway line and fed Mane who rolled it sideways to Everton striker Gueye, whose shot skewed off Cionek's leg and into the net.
Minutes after half-time, Sane was fortunate not to be sent off for a challenge on Lewandowski when he brought down the Polish striker as he honed in on goal. He escaped with a yellow card.
Krychowiak connected with Kamil Grosicki's cross to give Poland hope, but they were unable to make up the deficit despite four minutes of injury time.