The Jambos struggled to create much in the way of goalscoring opportunities and paid the price in what proved to be a disappointing afternoon at the Hope CBD Stadium.
Callum Morrison had one of the visitors' few efforts that flew just wide of the post in the first half but it was his side’s failure to work Gary Woods in the home goal that really irked Levein.
Hearts now trail fourth-placed Kilmarnock by four points with Aberdeen a point better off in the race for Europe. Capital rivals Hibs are also just two points behind after their victory over Motherwell.
“We didn’t create enough it’s as simple as that,” Levein said. “We started the game very slowly and our passing wasn’t enough to cause Hamilton any problems. I thought we dominated the game for long spells but it was going to be difficult because we gave ourselves a mountain to climb.
“Our final cross or pass was lacking in quality. We spoke before the game about second balls which are important when you come here so it was really frustrating.
“Our tempo and focus was missing. I’m concerned about our lack of aggression because we didn’t really have that competitive edge.”