Sadio Mane scored in the 15th minute of the encounter which was enough to hand the Teranga Lions a 1-0 win at the Cairo International Stadium.
The Liverpool forward had a chance to double the lead from the penalty spot in the 61st minute but his effort was saved by goalkeeper Denis Onyango.
“The most important thing was that we were able to score that early goal. Even though we didn't score a second, I think it helped us,” Koulibaly told Goal.
Uganda dominated the second half of the game as they pressed for an equaliser but the Teranga Lions held on to their first-half lead, frustrating the attacks of the Cranes, to ensure their qualification to the quarter-final of the continental tournament.
“It's true Uganda dominated the second half but we played our game. Uganda are a big team so we expected it from them,” he added.
Senegal will take on Benin, who surprisingly ousted Morocco out of the competition, in the quarter-final at the 30 June Stadium on Wednesday.
Victory over the Squirrels will boost the chances of the Teranga Lions claiming the Africa Cup of Nations for the first time in their history.