With Daniel Nti coming in for Mike Symons, it was otherwise the same side that beat Stockport County on Saturday.
City's promising start was soon shattered when Darryl Knight struck a lose ball into the right-hand corner from an acute angle to put the visitors ahead just before the half hour mark.
Just three minutes later, Bogle played a one-two with Moore on the left to fire home a second for the Moors leaving Carl Heeley's men with an early mountain to climb.
City were better after the break with Tristan Dunkley going close with a dangerous shot just wide of the far post, having tried his luck from just outside the area shortly before this, falling safely into the goalkeepers hands.
But once again City's promising work was undone. In the 66th minute defender Wayne Thomas unfortunately headed the ball into the back of his own net to make a bad night even worse for City.
Substitute Aaron Brown, who had been on the the field for a couple of minutes pulled one back for City, heading home from close range.
All hopes of an unlikely comeback were ended when Bogle netted a fourth for Solihull with a deflected free kick from the edge of the box, doubling his tally for the evening and sadly confirming the end for City.
Report by: Alison Deeley / Ellis Friend