The Red Devils extended their winless streak to four matches after failing to burst through Police's tight defense.
Their task was made harder when mercurial midfielder Mohamed Barakat received his marching orders six minutes past the hour mark for picking up two yellow cards.
He was initially booked for diving in the penalty area before being given the second yellow for lunging at an opponent.
Greisha's decision prompted Ahli fans to hurl insults against him but Al-Badri believes the official's errors were not costly.
"I can't say that the referee cost us a win. He did not make any prominent mistakes," Manuel Jose's assistant told reporters after the match.
"Our players played well but had bad luck in the first period and matters went from bad to worse when Barakat was sent off."
Ahli are still in charge of the table on 42 points, four ahead of second-placed Ismaili, who have a chance to narrow the gap to just one point if they beat Petrojet on Monday.
"The competition will be fierce in the upcoming games, but I don't want Ahli supporters to be worried because we are determined to keep our title."
The Cairo giants are looking to win a fifth consecutive crown.
Successful Defense
Police assistant coach Mohamed Ibrahim lauded his team's defense that put Ahli strikers at bay throughout the match.
"We were aware that Ahli will keep pushing forward during the whole game," he said.
"Credit to our defenders for successfully marking Ahli men. We succeeded in achieving our target of avoiding a defeat."
The draw moved Police to ninth place on 27 points, seven clear of the relegation zone as they enjoy a fine form under respected coach Talaat Youssef, who steered Gaish to a fourth-place finish last season.