The 'Green Army' dominated the match at Kenyatta Stadium, limiting the North African giants to zero attempts on goal.
But coach Dylan Kerr was, however, left infuriated by the visitors' anti-football tactics.
"Esperance came to draw, they used time-wasting tactics to frustrate us because they had come for a draw. It is something that I am not happy with; especially their goalkeeper who on multiple occasions took a lot of time to take a goal kick and the referee was just there.
"However, I am happy with the way my players played, it was not the best of preparations considering the fact that we spent seven hours in the jam. We could have scored six goals, but it was just a bad day. We will not be cowed in the second leg."
Gor Mahia will need a scoring draw to progress to the next stage. The return leg will take place on March 17 away in Tunis.
This is the second time this week that Kerr has attacked a goalkeeper for time wasting.