Gary Long was the first to arrive at Hull Combined Court after Hayley Gascoigne, 32, suddenly went into cardiac arrest in the concourse following family court proceedings last January.
Hull Coroners Court heard Mr Long admit to mistakes, including failing to recognise that the mother-of-four's heart had a shockable rhythm.
He said: "I find that hard to explain and I can't understand it myself."
The paramedic, 60, who retired last November, told the hearing that he had put "dots" on Ms Gascoigne, who was wearing a dress and leggings, to check her heart's electrical activity, but did not follow it up with pads, to shock the heart.
"What I should have done is cut the dress and put the pads on," he told the hearing.
"It was a mistake, I put the dots on Hayley because I was thinking of her modesty."
Mr Long also accepted that he left cardiac drugs in his car and had to wait for a second team of paramedics to turn up with them 10 minutes later.
The inquest heard that Ms Gascoigne from Baildon Road, Scunthorpe, became "really upset" when her case concluded.
She went to the toilet but when she came back to join family members she complained of feeling dizzy and sick. She later died in Hull Royal Infirmary.
In a statement her sister Charlotte Jones said: "Her eyes rolled back and she seemed to become rigid."
The hearing heard how her family urged Mr Long - who took four minutes from arriving at her side to starting treatment - to "hurry up."
A security officer and a retired nurse had already given her CPR, and police officers who were at court for a different case became involved.
Detective Chief Inspector Tony Cockerill said Mr Long appeared uncomfortable with the situation and he felt he should intervene, offering to give chest compressions.
He said: "I could tell, through experience of having dealt with medical colleagues for many years, that something did not appear right.
"Just from the expression on his face, something was not how it should be."
He told coroner Prof Paul Marks how he had overheard a female paramedic, who later arrived at the scene, ask whether Mr Long had brought his kit.
DCI Cockerill claimed the paramedic responded with words to the effect of: "I left it in the car. I'm sorry. I thought it was just some kind of fit."
The court heard from Dr Ian Richmond, who carried out the post-mortem examination, how Miss Gascoigne's death appeared to have been caused by a failure in the heart's left ventricle, which in turn was the result of the hypertensive heart disease.
It is known as a "silent killer" as there are no symptoms necessarily associated with it.
He confirmed that she had otherwise appeared to be a "healthy lady" at the time of her death.
Asked by counsel for Mr Long, Laura Addey whether the medical episode could have happened at any time, he replied: "Yes sadly it could."
The inquest continues.