Goals from Ryan Stevenson and John Sutton saw Hearts move into 10th place in the Clydesdale Bank Premier League.
Lomas conceded they failed to cope with Sutton and strike partner Michael Ngoo as they missed the chance to move third.
Lomas said: "We have let ourselves down and let down the fans who have come down to support us.
"We were under no illusion what was going to happen. We saw the second half against Motherwell when they pretty much went direct every time up to big Ngoo and Sutton and they caused us problems.
"But it wasn't just them two, it was all over the park. When you don't win your individual battles, you come unstuck."