Moshiri thinks the supporters deserve better but believes a tough run of fixtures and injury problems are factors behind Everton's poor run of results.
Everton were booed off after a 1-0 home defeat to Burnley on Sunday, which Moshiri described as the only "unexpected" loss of the campaign. It leaves the Blues 16th in the Premier League table with just seven points from their opening seven matches.
After that game, Koeman said he was not worried about his future and Moshiri has made it clear that the Dutchman has the backing of the board.
"We're in a bad moment - but we have played three of the four title contenders away," Moshiri told talkSPORT.
"(Burnley) was the only unexpected loss. The four pre-qualifying UEFA games and two group games on Thursdays haven't helped. There is mental fatigue and seven injuries.
"These are early days and Koeman has my total support. We have great fans they deserve better. We know the honest and objective expectations of our supporters and will not let them down."
Everton have already faced both Manchester clubs and Chelsea away from home in the Premier League as well as hosting Tottenham at Goodison Park. Their only point from those matches came in a 1-1 draw against City.
Things do not look like getting much easier for Koeman after the international break as Brighton, Lyon, Arsenal, Chelsea and Leicester are Everton's next five opponents in all competitions.