The Seagulls drew a blank at Hill Dickinson Stadium, their first 'nil' in ten matches going back to last season.
They hit post and bar, wasted a penalty, missed at least two clear chances and failed to make the most of other promising situations.
Everton had Jake O’Brien, a centre-back, operating on the right of defence, third-choice central defender Michael Keane alongside James Tarkowski and midfielder James Garner on the left.
Behind them, Jordan Pickford was arguably man of the match although much of the focus in that respect was on Jack Grealish.
Everton’s makeshift back-line was balanced to a degree by Albion’s lack of attacking options off the bench.
But Moyes’ words underlined the chance the Seagulls missed to get off to a seventh successive winning start away from home.
The Everton boss said: “The biggest thing for me was getting the result when we put a half-botched team out.
“We are having to play players out of position, we are really short on defensive cover at the moment and that’s a problem for us: Tarky with the hamstring (over the summer), Jarrad Branthwaite (out with a hamstring injury) and we’ve lost Myko (Vitalii Mykolenko) and Patto (Nathan Patterson) as well.
“We’ve been finding we are struggling defensively since the end of last season and we still are now. Garner’s performance was fabulous, his versatility is so important for us.”