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McKenna had waited for Sidaway to enter the park on 29 January with her dog, before crouching down in the bushes, ready to launch his attack.
A jury at Swansea Crown Court heard McKenna was "angry" after their relationship ended a few months earlier, and it was "luck" that she did not die, with her winter coat helping to save her.
During the trial, he told the jury he had put the newest, sharpest knife from his kitchen in his bag that morning, with the intention of using it to hurt Sidaway.
He said he wanted to cause Sidaway "serious harm" but not kill her.
"I felt she was reluctant to re-engage with me, and not even say hello," he said.
As she approached, he stabbed her multiple times, in what he agreed was "a rage of anger".
He told the court he was "shocked" at what he had done.
"I was aiming for her shoulder area and the upper body. I didn't want to kill her."
He said the attack was interrupted after Sidaway told him to stop and screamed, and a neighbour shouted.
Neighbour Susan Edwards told the court during the trial in July she heard "high-pitched screaming" and the "bushes shaking" before a man ran away.
Sidaway phoned for an ambulance and said: "I've been stabbed by my ex-partner... he's been stalking me".
McKenna fled the scene following the attack, and said he dumped his rucksack, with the knife, at an allotment near the park after he ate a yoghurt there.
He then walked to Bronwydd, a village about three miles (4km) north of Carmarthen, along the River Gwili.
"I found some shelter, a quiet woodland away from the road," he said.
"I was devastated and kept having flashbacks."
He said he was there for three nights, before he travelled via taxi and bus to a hospital in Aberystwyth.
