The Sky Blues fell to defeat at the Coventry Building Society Arena, despite a late comeback charge.
First-half goals from Karlan Grant and a Kyle McFadzean own goal pegged City behind at the break, leaving it all to do for the Sky Blues in the second half.
McFadzean pulled one back for the hosts late on, but City failed to find the crucial equaliser.
The Sky Blues started on the front foot, breaking down the right wing with Callum O’Hare who found Ben Sheaf on the edge of the box, but the midfielder was unable to connect cleanly with the strike.
The Baggies took the lead mid-way through the first half via Karlan Grant, who slotted past Simon Moore one-on-one, following Sam Johnstone’s long goal-kick.
Promising chances fell to the Sky Blues, before the half, most notably a fine piece of interplay between Viktor Gyökeres and O’Hare amounting to a chance for Todd Kane, whose deflected effort crashed off the woodwork.
A series of throw-ins proved a dangerous form of attack for the visitors, with the second of two ending up in the back of the net after a goal-line scramble, going down as a Kyle McFadzean own-goal.
HALF-TIME: Sky Blues 0-2 West Brom
The Sky Blues piled on the pressure after the break, well beyond the hour mark, etching out chances for O’Hare and Sheaf, with the best falling to Kane at the back post whose volley sailed narrowly wide of Johnstone’s post.
City continued to dominate possession in the second-half, keeping the visitors quiet in attack, and created an array of chances for theirselves, but lacked a finishing touch.
Kyle McFadzean pulled one back for the Sky Blues in the final exchanges, heading home from a corner, but the uphill battle proved too much for City on this occasion, as Gyökeres dragged wide from range for the final chance of the game.
FULL-TIME: Sky Blues 1-2 West Brom
SCORERS: Karlan Grant (20’), Kyle McFadzean (OG, 43’), Kyle McFadzean (83’)
YELLOW CARDS: Alex Mowatt (34’), Sam Johnstone (66’), Cedric Kipre (74’)
ATTENDANCE: 23,755 (4470 away)
Sky Blues XI: Simon Moore (GK), Todd Kane, Fankaty Dabo, Kyle McFadzean (C), Michael Rose, Ian Maatsen (Dom Hyam 45’), Ben Sheaf, Gustavo Hamer (Liam Kelly 40’), Callum O'Hare (Tyler Walker 77’), Matty Godden, Viktor Gyokeres.
Unused subs: Ben Wilson (GK), Jordan Shipley, Jamie Allen, Jodi Jones.
West Brom XI: Sam Johnstone (GK), Cedric Kipre, Kyle Bartley (C), Matt Clarke, Darnell Furlong, Taylor Gardner-Hickman (Semi Ajayi 87’), Alex Mowatt, Conor Townsend, Grady Diangana (Jordan Hugill 55’), Callum Robinson (Adam Reach 69’), Karlan Grant.
Unused subs: David Button (GK), Caleb Taylor, Rahaan Tulloch, Tom Fellows.