About two million people in the Perth, Peel and South West areas of WA were plunged into a five day lockdown on Sunday in order to stop any potential spread of the virus from the guard.
Mr McGowan said he was not afraid to apologise for the saga but defended the swift action taken after they found out about the case.
“I’m very sorry for what’s occurred,” he said.
“This has been debilitating for lots of people. Obviously we went for 10 months without a single case and everyone in WA was very happy about that, this has been a shock to all of us.
“We have swung to action very quickly , [on Sunday] within a matter of hours we put in place a huge number of rules.”
Mr McGowan also admitted he would have been wearing a mask if he was in the hotel but did not place blame on the guards who had just been following health advice given to them by authorities.
“If I had been in a hotel I would’ve worn a mask,” he said.
“Obviously the security guards have been following the rules that have been put in place by the infectious disease experts.”
Mr McGowan defended the health advice given to the state, which he said had held the state in good stead for the past 10 months.
“Over the last year we have had the best outcomes of anywhere in the world, obviously this has been a significant setback,” he said.
Outside of the existing lockdown mask requirements quarantine security guards will now also be required to wear masks at all times while working.
If WA continues to record no new cases over the next two days it is likely the lockdown will end by Friday but Mr McGowan said some restrictions including gathering limits would likely remain.
He said it was expected the government would announce the new restrictions by Friday morning.