VIDEO: Elgin must bounce back
Price blamed poor defending at free kicks and corners for City's demise at Broadwood.
Clyde surged into a 3-0 lead through defender Martin McNiff's double and a David Goodwillie strike, before ex-Clyde man Jordan Lowdon pulled one back on half time.
The visitors were unlucky not to further reduce the deficit with Rabin Omar hitting the bar, before the former Annan midfielder was sent off for two bookings.
The home side then notched a fourth goal to seal the points and leave Price counting the cost.
"It was uncharacteristic losing two goals from pretty simple corner kicks," he said. ""We should have been better at dealing with that.
"Now it's about making sure you don't go on a run of defeats. It's about bouncing back straight away which I'm sure we are capable of doing."
Omar will be suspended for Saturday's home clash with Queen's Park, who recently parted company with manager Gus Macpherson when he left to take up a position at St Mirren.
Mark Roberts has taken over as caretaker boss and will lead the Spiders into action at Borough Briggs.
More City news in Friday's Northern Scot