The win sets up a crucial showdown with Kerry later this month and simultaneously condemned Carlow to Christy Ring Cup hurling in 2017.
Kelly said he had endured a miserable six days after the county’s shock defeat to Westmeath in Mullingar on May 1.
“I don’t ever want to have a week like it again, where you have cowards ringing you off private numbers and the stuff that got thrown at me over social media.”
He also said that a number of players had quit the squad after the 14-point loss to Westmeath.
“We had three lads walk away with the comment they didn’t like where this thing is going and that they don’t want to be associated with it. What you have left in the dressing room are very honest fellas, and they’re working very hard. There’s nobody cutting any corners, they’re making a huge effort.”
It could all have been very different for Offaly, who trailed by a point at half-time.
But the brilliance of Shane Dooley — who hit 1-10 — dragged Offaly to safety.
Dooley scored seven of those points in the first half but his side still trailed by 1-7 to 0-9 thanks to a Ross Smithers goal, and Carlow could have pulled clear after half-time but failed to do so.
Carlow boss Pat English said: “We missed 1-4 or 1-5 straight after half time, you’d want to be getting some or even half of that, but that’s the story of sport, you have to take your chances.”
While Sean Murphy scrambled home a goal to put Carlow three points up, Offaly responded in kind with the very next play — Dooley tapping the ball home after excellent approach work from Joe Bergin.
A brief purple patch saw Offaly go three in front by the start of the fourth quarter but Carlow continued to hang in there and it was only when Diarmuid Byrne, Hugh Paddy O’Byrne and goalkeeper Brian Treacy saw straight red cards late on that home fans could breathe more easily.
S Dooley 1-10 (0-6f, 0-1 ’65, 0-1 s/line), J Bergin (0-1f), P Murphy and J Mulrooney 0-2 each, K Connolly 0-1.
S Murphy 1-1, R Smithers 1-0, J Doyle 0-3, K McDonald (0-1f) and D Byrne (0-1f) 0-2 each, S Murphy, JM Nolan and D Byrne 0-1 each.
J Dempsey; P Rigney, D Shortt, C McDonald; D King, S Gardiner, D Mooney; P Camon, S Cleary; C Kiely, J Bergin, S Kinsella; P Murphy, S Dooley, K Connolly.
J Mulrooney for Kiely (46), P Guinan for Cleary (56), J Sampson for Connolly (58).
B Treacy; G Coady, M Ryan, A Corcoran; R Kelly, R Coady, J O’Hara; J Doyle, D Byrne; Sean Murphy, Seamus Murphy, JM Nolan; R Smithers, M Kavanagh, K McDonald.
D Murphy for McDonald (46), HP O’Byrne for Nolan (60), C Lawlor for Kelly (70).
James McGrath (Westmeath)