City went into the clash at the John Smith's Stadium in the Championship's drop zone, but a 3-1 victory over manager Lee Clark's former employers secured a fourth win of the season and pulled the Midlands club clear of the bottom three.
Bartley proved the difference as he headed home a second-half double, but the defender was keen to divert any personal praise.
"First and foremost it's fantastic for us to get three points," he told the club's official website. "It's clear that we needed it and the lads have worked really hard in training and the gaffer and all the coaching staff have pulled together. It's a fantastic performance.
"In the dressing room there's a lot of team spirit, a lot of togetherness and I think we showed that out there.
"I'm over the moon to get two goals but, first and foremost, it's the three points. The lads have worked so hard and we deserve it."
But Bartley was left to reflect on what turned out to be a mixed afternoon on a personal note against the Terriers.
Having celebrated his second goal in front of the travelling Blues support, the on-loan Swansea centre-back was shown a cruel second yellow card and subsequent red for simply stepping over the advertising hoardings before re-entering the pitch seconds later.
"I've obviously scored to make it 3-1, the lads have come over to celebrate with me, I was about a yard away from the boards and I've just taken one step over, one step back and the ref sent me off," Bartley said.
And Blues boss Clark was left frustrated by the dismissal, which will see Bartley suspended for Saturday's visit of Blackpool.
"Football is an emotional game. Kyle hasn't enticed the Huddersfield fans. He has gone to celebrate with his own fans and common sense should prevail," he said.
"Probably under the rules the referee had no option but you have to be allowed to celebrate. That's what the fans want to see."