The young Foxes, who are currently fifth in the U18 Premier League South division, went into the clash following a 4-4 draw with Manchester United and a 3-2 loss to Brighton & Hove Albion in Group F.
It was the hosts who took the lead at the Club's training ground as Dempsey Arlott-John linked up well with Terell Pennant with the latter showing composure to find the net in the 27th minute.
However, despite leading for the majority of the clash, the Baggies hit back in the final moments as Irish striker Alex Gibson and then a trialist converted in the 83rd and 87th minutes to seal victory.
As a result, City's youngsters, who had Shane Flynn sent off for second bookable offence with 15 minutes to play, finish in fourth place in Group F and will now concentrate on their respective campaigns in the U18 Premier League South and the FA Youth Cup.
Next Friday, they head to Brighton & Hove Albion for a third round FAYC tie at the Amex Elite Football Performance Centre (7pm kick-off) before visiting Aston Villa on Saturday 14 December (11am kick-off).
The details...
City: Bosworth, Gyamfi, Flynn, Barrett, Sams, Leathers, Maswanhise, Tavares (Murch 60'), Arlott-John (Loughlan 78'), Ewing, Pennant
Subs not used: Odunze, Fitzhugh, Russ
Goal: Pennant 27'
All times GMT.