First-half goals from Lyle Taylor and Aaron Taylor-Sinclair were enough to condemn administration-hit Hearts to a 2-0 loss.
It was the Edinburgh club's sixth defeat in their last seven league games and leaves Locke's men 19 points adrift at the foot of the table.
They are yet to break even following their 15-point penalty during the summer and only have 17 games left to attempt a miraculous escape.
Locke is not throwing in the towel, but knows a big chance of closing the gap was missed.
"We have got to keep going, the mountain has just got bigger," he said.
"We have got to keep working hard, that was the disappointing thing for me today, we can't just turn up for 45 minutes.
"It's extremely difficult. That was a big game.
"But we have got to keep going, there is nothing else we could do."
- Sports & Recreation
- Lyle Taylor