First off, he DID use his Force powers, or at least tried, (ultimately, unsuccessfully), at that critical moment:
Unarmed, he raised a hand and utilized the Force to fend off one slashing blow after another, until finally her fury penetrated his remaining defenses. Taking a glancing blow to the head and chest, he went down, a prominent burn slashed across his face. Weakened, he reached out toward his lightsaber, trying to draw it to him. (all quotes are from Foster's novelization)
He also used them before, when he force-threw Rey against a tree (which knocked her out - which is why he was fighting Finn before her in the first place).
As for why he didn't fight as well as his talent and training and past performance indicated he could/should have:
He wasn't firing on all cylinders.
He was emotionally compromised[1] from killing his father. He got shot in the side with a bowcaster as a result.
Stunned by his own action, Kylo Ren fell to his knees. Following through on the act ought to have made him stronger, a part of him believed. Instead, he found himself weakened. He did not hear the roar of the enraged Wookiee above, but he did feel the sting of the shot from the bowcaster as it slammed into his side, knocking him back on the walkway.
He is facing a Force prodigy that he's ambivalent about. He effed up pretty much non-stop since the start of the film (including having his mental ass kicked by said Force prodigy) and his Darthk Mentor isn't very happy with him.
There was as much curiosity in Supreme Leader Snoke’s voice as there was disappointment. “This scavenger—this girl—resisted you?”
“That’s all she is, yes. A scavenger from that inconsequential Jakku. Completely untrained, but strong with the Force. Stronger than she knows.” His mask off, Ren replied with what seemed to be his usual assurance. No one else would have sensed a difference. Snoke did.
The Supreme Leader’s voice was flat. “You have compassion for her.”
“No—never. Compassion? For an enemy of the Order?”
“I perceive the problem,” Snoke intoned. “It isn’t her strength that is making you fail. It’s your weakness.” The rebuke hurt, but Ren didn’t show it. “Where is the droid?”
Smooth and unctuous, the voice of General Hux rang out in the assembly hall before Ren could respond. “Ren believed it was no longer of value to us.” Turning, the quietly livid younger man followed the approach of the increasingly confident officer.
“He believed that the girl was all we need. That he could obtain from her everything necessary. As a result, although we cannot be certain, it is likely that the droid has been returned to the hands of the enemy.”
Though visibly angry, Snoke’s tone remained unchanged.
and
He had to see for himself. As he strode down the corridor where walls of exposed igneous rock alternated with panels and consoles of metal and spun synthetics, Ren’s emotions were boiling. His present mental state contradicted all of his training, but he could not help himself. He had reacted poorly to what had happened earlier, and that had been reflected in the Supreme Leader’s judgment. To add to the discomfort, that slimy sycophant Hux always seemed to appear at the most awkward possible moment.
He gritted his teeth, angry at himself. It was a measure of his current weakness that something like jealousy toward an insignificant simpleton like Hux could even enter his mind. It was nothing but a waste of physical energy and mental concentration. Hux—Hux was not worthy of such attention.
The girl, on the other hand…
This, if you recall, is followed by an epic tantrum trashing the room with his lightsaber.
Initially, he wanted to convert Rey.
Ren held his lightsaber, poised to strike. “I could kill you right now. But there is another way.”
Breathing hard, Rey looked up in disgust at the man looming above her. “You’re a monster.”
“No. You need a teacher.” He was beseeching and insistent all at once. “I can show you the ways of the Force!”
Afterward, she basically outfought him to the point he was unable to do anything, by pretty much using Dark Side of the Force (strongly echoing Luke's defeat of Vader on board Death Star 2).
A long moment passed, in which Ren sensed a change in the air, a change in her. Then she opened her eyes and attacked, viciously, in a way she didn’t know she was capable of, striking again and again as Ren was slowly driven back. The flaring energy from the interacting lightsabers was more pronounced than ever in the flurry of her attack. And - Ren went down.
He was up again in an instant, but not in time to fully deflect a following blow from Rey’s weapon. He succeeded in blocking it, but he still took the full force of the strike against the haft of his own lightsaber. The weapon went flying into the snow.
[1] - see what I did there? Star Trek reference in Star Wars answer! And both J.J. Abrams!
