The Reds took the lead through Ronan Darcy’s early strike, but Callum Morton’s first half double ensured Rovers claimed the win.
The 2-1 defeat meant Crawley failed to win a single game in October, a run stretching across six games in all competitions.
Lindsey was left furious by the manner of the loss, saying the Reds ‘gifted’ Rovers their goals.
But the Crawley boss vowed he would right the Reds’ defensive wrongs amid rumours linking him with the vacant post at Gillingham.
He said: “Frustration would be a word I would use. We started off great. We did a lot of work in how we wanted to play, how we wanted to attack, how we wanted to press. I thought we did it brilliantly for large parts of the first half.
“We scored a good goal to put us in front, and then we gift a first goal. It’s a gift.
“Our detailing in our passing out from the back was not on point today. In my opinion we’ve gifted them two goals.
“The second half becomes harder because of that, because of those two reasons, because those two goals that we gifted them.
“We’re not as free-flowing, we’re not as attacking, we’re not as aggressive. They make it hard because they’ve got something to hold onto and it becomes a hard game.
“Forest Green didn’t beat us today, we beat ourselves and that’s the disappointing thing for me.
“I’m sick of saying these words. When it’s 1-0, we need to be better. We just can’t gift goals like we do, and it’s individual error.
“We can’t keep on playing well and losing games, but I’ll put that right.”
Lindsey also paid tribute to all the Crawley supporters who made the trip to wet and windy Gloucestershire.
The Reds boss reiterated his appreciation to the fans of the club, and admitted he was disappointed his players couldn’t secure a result the supporters ‘deserved’.
Lindsey added: “I made sure I stood there and clapped them for a decent period because I really do appreciate it.
“The fact they stand in the rain, we didn’t give them the three points that they deserved. They deserve the three points, those fans who stood there in the rain all afternoon.
“I made sure I got wet with them. I was only there for a couple of minutes but I didn’t want to just go over, clap and then walk in.
“They deserve far more than what they got today, the supporters, for sure.”