King, 66, who is retired from the hospitality industry and still lives in the town, was mightily impressed as he watched on while Shrewsbury got over the line to safety last term despite their absent boss.
Cotterill missed four months after contracting Covid-19. He suffered a serious bout and extreme after effects, which included two spells in hospital.
Glasgow-born King, who managed Shrewsbury and Telford after more than 300 appearances as full-back for Salop, hailed the achievements of the former Bristol City chief, who was appointed in late November.
"They were second-bottom when he took over, and anybody who takes over someone at the bottom and gets them into that position has done a fantastic job," King said. "It doesn't matter who the manager is, he's done a fantastic job.
"To do it when he's had Covid, and he's been in intensive care, when he's been managing on the phone, it's been a miracle really.
"To get them out of trouble is brilliant, to do it when you're ill, and to keep talking to your coaches? Fantastic.
"I go to the local pub and they're all Shrewsbury supporters, when he'd got them out of trouble they were all putting little bets on to get in the play-offs!
"They weren't far off, only nine or so points at one time, you start looking at who you are playing next – which you shouldn't do in football.
"You can struggle against teams at the bottom but they played the teams at the top and beat them all, Blackpool, Sunderland, Hull, Lincoln."
Cotterill continued to manage Town from afar, working on all phases of training and match preparation, as well as team talks and tactics during matches, for which he earned significant for putting his body on the line.
A turnaround in results, which included three consecutive 1-0 wins at three of the top four, lifted Shrews well clear of the mire by New Year. And Shrewsbury continued to earn crucial wins through February and March, eventually finishing 17th.
"They started well and were winning and getting good results, that spreads around the club," King added.
"The coaches were taking over and the manager was talking to them, when you have a run of positive results then everything starts to look rosy around the club and that's what happened.
"They had some brilliant results and that breeds confidence and other wins.
"If they were getting beat and the manager went away then that's a different story."