Peter Haring headed the hosts in front after a dominant opening 25 minutes. However, the lead was short-lived with Hibs equaliser through Daryl Horgan after he turned in Marc McNulty's cross three minutes later.
Hearts would never again enjoy the kind of territorial advantage they had prior to the equaliser and had no answer after falling behind to Horgan's second goal of the game.
McNulty was offside in the build up to Hibs' first and the home side could have had a penalty when Stephane Omeonga caught John Souttar right at the end of the first half, but Levein only wanted to focus on his side's failings rather than blame the officials.
He said: “It was hard to take. I was pleased with the overall performance, thought the first half was better than the second but we just didn’t score enough goals to put the game to bed. We’ve played worse in derbies recently and won.
"The reasons we’ve lost the game are down to our wastefulness in front of goal. We needed a second to put us on what should have been easy street but the more we missed, the more I thought it’d be one of those days.”
“Hibs scored with their first two shots on target, which is clinical. And we were the exact opposite."