Allen, the UK Championship and Northern Ireland Open champion, entered the event in Wolverhampton as one of the favourites following Ronnie O'Sullivan and Neil Robertson's failure to qualify.
But the 36-year-old was far from his best at Aldersley Leisure Village which was taken advantage of by England’s O'Connor - the lowest-ranked player in the draw.
O'Connor moved into a 3-0 lead after opening with a solid break of 63.
Allen put his first frame on the board just before the interval and then cut the gap to 4-2 before O'Connor hit back with an excellent clearance of 132 to extend his lead.
With his chances fading away, Allen took the next frame to give him a glimmer of hope but it wasn’t to be as O'Connor claimed victory in the ninth.
The other match on Monday saw Ryan Day, the British Open winner, earn a 6-2 victory over Chris Wakelin.
The pair exchanged frames up until the sixth where Day rattled off four straight to advance.
