Killie had led after going behind but Jackie McNamara's men found another gear to power themselves into the fifth round with a 5-2 win.
Johnston was pleased with his side's spirit, though, despite the lop-sided nature of the scoreline.
"I feel sorry for the players," he said. "They put in so much effort but it looks like they have been hammered.
"In reality, it wasn't really a hammering because we played a lot of good stuff. I think we can take a lot of heart from our performance.
"There were some positive parts which we can take in to the rest of the season as we had a very young side out there."
United full-back Andrew Robertson's opener was overhauled by goals from Darren Barr and Chris Johnston, but Stuart Armstrong drew the sides level again before Robertson grabbed his second of the night to make it 3-2.
Substitute Brian Graham's penalty and Gary Mackay-Steven's drive secured victory.
- Sports & Recreation