Ryan Stevenson has suggested Hearts became complacent in their bid to confirm third place in the Clydesdale Bank Premier League.
Hearts held a 15-point lead over fourth place at one point this season and were considered genuine threats to title-chasing Celtic and Rangers.
However, after losses to each half of the Old Firm saw their hopes of a title challenge end, Hearts have recorded one win in their last five games to give Dundee United hope of overhauling their rivals.
Stevenson said: "It looked so easy at one stage that we were definitely going to get there. It's been tough. When you open up that big a gap, you maybe switch off and think we're 12, 15 points in front, we're fine.
"The gap closes very, very quickly. Dundee United have shown how good a team they are and pressed back. We managed to get a little bit of luck on Wednesday night (United lost 2-1 at Motherwell).
"We know that if we go off the boil Dundee United will be right on our tails. For us personally we've got to take it every game at a time."