Charlie MacDonald gave the O's the lead after nine minutes with his first goal for the club since arriving from MK Dons a month ago.
Then, having missed a penalty in the 15th minute, midfielder Martin Rowlands struck a stunning volley to double the host's advantage midway through the second half.
Substitute Michael O'Halloran goal had been on the pitch for just five minutes when he blasted home from close-range with 15 minutes remaining but it proved too little, too late for Rovers as they went down 2-1.
"We were disappointing, we never got going and we were second best all afternoon," said Moore, whose side remain top of the table despite losing. "Fair-do's to them, they scored a good goal but we are miles better than what we showed. We were so weak from set-plays and we allowed too many crosses to come in.
"It's a shame because if we are not careful, we are going to let something slip that has been a bit special for us.
"That performance was unacceptable from us. When we concede a goal at the moment, it looks as if it could be one-two-three because basically we are too soft and too soft-centred. The two centre-backs were weak and they have got to be stronger, the full-backs were poor and that back-four have been our strength.
"We've let Orient boss us and that's disappointing. Every time they had a free-kick it looked as if they were going to score and we have to start taking responsibilities, there's no doubt about that.
"We were lucky to only be one-nil down at half-time, we got out of jail really. We were desperate for the interval to come, although I don't think Russell Slade would have been.
"We started to have a little go in the second-half but we conceded another sloppy goal and although we got a goal to get us back in the game, the quality in the end wasn't good enough."
- Sports & Recreation
- Martin Rowlands