The Dons missed a golden chance to take a 10th-minute lead when Hibs goalkeeper Ben Williams saved a Niall McGinn penalty and neither side was able to break the deadlock after that.
"We didn't play well today, but we picked up a point and a clean sheet which is the real positive, but Aberdeen were the better side," Fenlon said.
"We need to make sure we start games better, but we've said that the last few weeks.
"When you're under the cosh like that, you maybe do feel like it's a matter of time, but the penalty save maybe gives us a bit of heart.
"They were sharper than us, and had better movement than us at times. They've got a lot of pace in the wide areas, but we defended well, the goalkeeper did well for us and I thought the two central midfielders worked tremendously hard. We didn't create enough going forward, though."
Hibs' on-loan Manchester City defender Ryan McGivern was substituted at half-time due to injury.
"Ryan felt his hamstring tighten up," added Fenlon. "He could probably have played on, but with the run of games coming up it wasn't worth the risk."