A much-changed Latics line-up showed up better than in the 2-0 Championship defeat at the Hawthorns, but ultimately suffered the same fate.
Bakary Sako scored the only goal, just after the half-hour mark, with a free header from Chris Brunt’s cross that went in off the underside of the bar.
Latics had squandered several chances before that to take the lead, with Callum McManaman, Will Grigg and Chey Dunkley all coming close.
But once again Paul Cook’s men were punished for their profligacy, and fired a blank for the sixth time in their last seven matches in all competitions.
The one positive is that Latics can now firmly focus on their priority this season - the league - without the worry of being temporarily distracted by the FA Cup as they were last term.
Having made seven changes to the starting XI, Cook saw his Latics team fly out of the blocks and take the game to their hosts.
McManaman, making only his third start of the season, cut in from a short corner only to see his shot deflect past the post.
A great ball from McManaman into Grigg saw the striker - wearing the captain’s armband for the day - pull the trigger, forcing a decent save from Jonathan Bond.
From the resulting corner, Dunkley headed inches over, with the home side having barely touched the ball in the opening 11 minutes.
Nice hold-up play by Grigg opened up a chance for Lee Evans, whose shot was well off target.
At the other end, a Brunt cross was cut out by Dunkley to Jonathan Leko, but he could only bundle it wide from close range.
With half an hour gone, the visitors would have been more than pleased with how things were going.
Typical of the season, though, Latics were made to pay for their lack of cutting edge by falling behind.
They received a warning when Brunt curled a beautiful free-kick over the wall, with the fingertips of Jones sending it over for a corner.
But the respite was only temporary as Brunt’s delivery was nodded home by Sako, via the underside of the bar, despite the best efforts of Jones.
The Baggies were lifted by their breakthrough and Latics spent the last 15 minutes of the half on the back foot, albeit without further damage inflicted.
To be fair to Latics, they started the second half brightly, and a Kal Naismith free-kick looked inch-perfect for Dunkley at the far post.
However, the big centre-back appeared to lose the ball in flight and the ball drifted out for a goal-kick.
Dunkley made amends moments later when West Brom looked odds-on to double their lead through Sako.
After being initially denied by Jones, Sako lashed the ball towards an empty net - only for Dunkley to somehow get the ball off the line in acrobatic fashion.
Latics dodged another bullet when Leko raced clean through only to slide the ball past Jones and also the far post.
That was the signal for Latics to make their first change, Reece James coming on for Leo Da Silva Lopes, and slotting into the centre of the midfield.
And the on-loan Chelsea man settled into his new surroundings with effortless ease, forming an effective barrier in front of the back four and also looking to release the attack with long and short-range passing.
One example of this had to be seen to be believed, the 19-year-old breaking up a promising Baggies break with a textbook challenge, holding off his opponent with a shoulder charge, before unleashing a 60-yard ball straight into the stride of Josh Windass out on the left-hand side.
Unfortunately, not enough of James’ team-mates were making their own points, and debutante Mason Holgate almost made it 2-0 only to head just over.
Gary Roberts took over from Callum Connolly, and McManaman gave way to Shaun MacDonald, who was making only his second appearance of the season.
But Latics couldn’t find the goal that would have earned them a replay later this month.
They came close when a Windass shot flew just past the post, with Grigg agonisingly close to getting a touch that would surely have sent it goalwards.