Peterhead spent a miserable midweek night at Galabank fighting doggedly against an Annan side who moved second with their 2-0 victory.
The match, the first time in this league campaign that the Toon failed to score, was marred by defensive errors.
Teenager Josh Todd, signed from Carlisle earlier this season, scored his first home goal when he fired in on 62 minutes.
Young Peterhead defender Ryan McGeever then ended what was for him a torrid game with a headed own goal from Andrew Mitchell’s corner 20 minutes from time.
Bryan Gilfillan came closest for Peterhead but the Toon rarely threatened.
The defeat brought to an end a three match unbeaten run for the visitors.
After the match Toon goalkeeper Graeme Smith, yet to keep a clean sheet this season, said: “We weren’t great but we were holding our own.
“Then we conceded a soft goal which gave them a lift and then after that we were chasing our tails.
“We huffed and puffed but I can’t remember their goalkeeper having many saves. It was frustrating, one of those frustrating midweek fixtures.
“The two goals were poor from us, especially the first one which gave them a wee edge in the game.
“Then we’re chasing even though before that we never looked in any serious danger.”
The team were clearly disappointed to have let slip a chance to move into the playoff places, instead granting that opportunity to the Galabankies.
Jim McInally said: “I didn’t feel we had done enough to score.
“We passed it around well but I didn’t see enough in us.
“What i saw was rory being isolated up there and he wasn’t playing well but was working hard.
“I also saw a team who have not been playing regularly. It’s been a strange few weeks with playing and not playing.
“It was one of those games where the first goal was always going to win it.
Dont’ get me wrong, at half time I couldn’t see us losing the game. I just never thought we looked as though we’d get in behind.
“I’m not going to criticise Ryan McGeever - you have got to remember he’s 19 and he’s had a virus and he looked as though i needed to get him out of there and take the pressure off.
“He just struggled a wee bit and I thought I’d put tully in yesterday to give some experience and put Jamie Redman back to give us some aggression and it all came good.”
Peterhead: Smith, Sharp, Richardson (McGlinchey), Redman, Noble, McGeever (Buchan), McCann, Cowie, Gilfillan, McAllister, Brown.
Unused: Jarvie, Fitzgerald, Alexander.
Referee - Andrew Dallas
Attendance - 277