The Steelmen fell behind to a Goldy Capela goal 12 minutes into the second half, only to equalise soon after through Charlie Wise.
However, the hosts grabbed all three points thanks to Charlie Smith’s late goal.
With second-placed Berkhamsted winning, the Steelmen’s lead at the top of the BetVictor Southern League Division One Central was cut to two points.
And they now face a huge game against third-placed Halesowen Town at Steel Park next weekend with the Yeltz six points behind Corby but with four games in hand.
However, there will be some soul searching to be done between now and then after a disappointing loss at Barton.
“It’s very frustrating,” said joint-boss Robinson.
“Last week (the 5-2 win over Aylesbury United) we had a good performance and this week we knew it wasn’t going to be pretty, the pitch wasn’t great.
“When you come to this place you don’t expect three points but you expect a better performance than the one we put out.
“I don’t like to mention officials but there were a few big decisions that cost us. However, our performance wasn’t good enough. You have to grind out results and that’s something we haven’t done on this occasion.
“The players won’t accept a performance like that and we won’t let them accept it. Everyone is deflated and it was out of character from what we are.”
Fellow joint-boss Mulligan, as usual, was on the pitch for the game and felt those key decisions were crucial to his team.
But he conceded the display wasn’t up to scratch and he knows the importance next weekend’s clash now carries for his team.
“I thought the one from Elliot (Sandy) was half a yard over the line, then they have cleared one off the line with one of their player’s hand and then Steve Diggin tells me he has been kicked in the ankle and that should have been a penalty,” Mulligan said.
“I don’t really want to dwell on it and say that is what made us lose the game because it hasn’t.
“Overall, we probably haven’t been good enough to win the game. We needed to be solid and we weren’t.
“We will have a look at the video and see what went wrong.
“We will prepare for next week, it’s a massive game next Saturday. Nothing is won in the middle of January but we will need to go and win if I am being honest.”