Goals from Paul Green, the returning Joe Leesley and Jordan Burrow saw the Pilgrims move up to fourth in the National League North, but they had to do it the hard way as Connor Kennedy and Jordon Crawford put the Poppies 2-0 up with seven minutes gone.
"Mixed emotions, to be 2-0 down after seven minutes, bit of a shock," Elliott told BBC Radio Lincolnshire.
"But that Paul Green goal changed everything, and what a really good day. I thought the fans were brilliant and the result was even better."
United stretched their winning run to three games and recorded back-to-back away victories for the first time this season, even it Elliott confessed he needed 'to have a few words' at the interval following what he deemed a poor start.
"I didn't feel Kettering came out and blew us away, I thought we were sloppy ourselves," he added.
"First goal, Tom Platt's lost his man, that can happen. Then we had a little wobble, but that Paul Green goal gave us confidence and I thought there was only one team to go on and win it."
Elliott was full of praise for fellow Pontefract lad Green, the former Republic of Ireland international still doing the business at 38.
"He's ridiculous," he added.
"I've known him since he was 10-11 years old and he's no different now, just full of energy and never stops. I thought he was the best player on the park.
"He's having a great season and just seems to get fitter and stronger as he goes along."
Elliott added he was 'really pleased' for Leesley to make his return with the leveller, coming in for the suspended Scott Duxbury.
There was also praise for Borrow, grabbing the winner on his 50th appearance for United.
Elliott said: "He deserves that goal, he's been brilliant for the last few weeks and he was excellent today, what a great winner.
"He's one of them players that players appreciate. He was one of the players driving it at half time, a proper leader as well."
Elliott also gave the thumbs up to the United support, continuing: "I'm glad there's a good turnout today, we're on a roll and need the fans with us.
"I hope they appreciate the unbelievable character the players have shown to come from 2-0 down against a difficult team.
"A really positive day for the club."