The 53-seater coach, which had transported tennis players from the Wirral, near Liverpool, became stuck down Crescent Fields, adjacent to Town Walls, as it tried to leave Shrewsbury Lawn Tennis Club.
Police were called to the scene just before 8.30pm on Tuesday as more than a dozen vehicles were left trapped in the club's car-park behind the stranded single-decker coach.
After about three hours police officers, with help from members of the Shropshire Horticultural Society, were able to use bolt cutters to open a gate which meant cars could then leave via the Quarry on Victoria Avenue.
Onlookers said the coach was "completely jammed" and emergency services said the vehicle's power steering had also failed.
Mike Willmott, 64, a former English teacher who was working on his nearby allotment at the time, said a wall stopped the driver from getting the coach back up the lane.
"It was the sat-nav which caused the driver the problems and how on earth he got the coach down that steep and tiny lane in the first place is beyond me," he said.
"It must have been a scrape for him the first time but there was no chance he was making that turn back out and it was just so funny seeing a massive coach completely jammed in."
Richard Ewels, a spokesman for West Mercia Police, said: "It was leaving the car-park but became wedged across the road, blocking the road and preventing vehicles from entering or leaving the car-park.
"It is believed the power-steering had also failed but the coach driver arranged for passengers to transfer to another coach."
He added: "Police eventually managed to open several gates through to the Quarry Park where the cars were let out after more than two hours."
Susan Barker, who was competing, said up to 15 cars had been trapped in the car-park.