Hibs went into their fifth competitive game of the campaign looking for their first goal on the back of four successive defeats.
Scott Robertson's strike nine minutes from time cancelled out a Stuart Armstrong goal to earn a valuable point on a day when Hibernian midfielder Kevin Thomson and United defender Gavin Gunning were dismissed for violent conduct after raising their hands to each other.
"I suppose that we scored and picked up a point, there is a bit of relief," Fenlon said. "But it wasn't a great performance to be honest with you, especially in the first half, when we were very, very poor.
"The sending-off seemed to galvanise us for some reason and we seemed to get going. I don't know why that happened. Afterwards we wanted to fight and scrap for the ball. But we didn't want to do that before."
United boss Jackie McNamara felt the incident leading to the red cards was a turning point in the match.
McNamara said: "I have spoken to Gav and he said he didn't throw a punch. The referee said that they were fighting, so you can take what you can from that.
"I think the two of them adopted an aggressive manner, which merits a yellow card. It changed the game and gave their crowd something to cheer about."