Kellock's men took England to the wire but eventually succumbed to a Chris Ashton try and fell to an agonising 16-12 loss.
"Obviously it was gut-wrenching to lose to England but from the support and messages we've had I think everyone could see we gave it our all, but it was not quite enough in the end," said Kellock. "We left nothing out there and can take some solace from that.
"The loss still hurts and the body is still hurting. I'm delighted to be back and see my family, as are all the boys, but it's tough. We wanted to be out there and still involved in what has been a great tournament."
The Glasgow lock has grown tired of Scotland falling at the last hurdle and is determined to ditch the tag of valiant losers.
"We're all getting fed up (of people saying Scotland are improving)," added Kellock. "Before the tournament we talked about where we wanted to be and how we wanted to come home. We didn't want to be back at this stage but we are - that's the reality.
"It's now about refocusing and everyone is looking forward to going back to their clubs. It was a good result for Glasgow (against Cardiff) last weekend and there was the historic win over in Leinster.
"I've been keeping in touch with the boys and it's great to see Johnnie Beattie back playing. The World Cup will stay with us, it was a great experience, but now it's about club rugby and Glasgow for me."