The Dons took the lead through Jack Rudoni in the 26th minute.
However, two second half goals in two minutes from the hosts saw Wimbledon’s lead evaporate before Alfie May added a third for Cheltenham.
The Dons slipped into the bottom four for the first time this season after Gillingham drew 0-0 with Sheffield Wednesday. They have 33 points, three more than Doncaster Rovers.
“We need a wake-up call,” Wimbledon head coach Robinson told the club’s official website. “We haven’t been in there [the relegation zone] all season – we have gone in there now.
“The 19 league games [without a win] is just not acceptable – I am embarrassed by it myself and hurting.
“This [dropping into the relegation zone] needs to change it. I will fundamentally keep working with the staff to give them everything, but they [the players] play the game when they go out there.
“That’s not me throwing them under the bus, but they do play the game. I ask them: ‘Do they feel as though they are getting enough from us to win games – tactically and in everything we do?’, and I get the same answers.
“But when they cross that line, they have got to play the game. For 80 minutes today, I don’t think we were at our best, but we were fine and looked comfortable.
“But we have walked off the pitch, and we have lost 3-1, and it ain’t good enough.”
Wimbledon are now a point from safety and without a win in all competitions in their last 20 games.
When asked if his side’s winless run was a mentality problem by London Online News, Robinson added: “It has got to be something, hasn’t it?
“All we keep trying to drive through is to relentlessly keep doing the same things.
“I have got to look at the goals, and I have got to look and see if it’s key areas. For me, there are too many little momentum changes with us – that’s my biggest problem.
“There are times when we don’t come out with the ball in one against one duals – we lose momentum there.
“There are times when we don’t run in behind, and when we don’t run in behind, we don’t spend enough time in their defensive third – that changes momentum.
“There are times when we get on the ball, and we under-hit balls.
“I don’t see this collective being dragged all over the place, I am seeing tiny little momentum changes, and we have to find an answer to that.
“I don’t think it’s just one big thing where we get pulled apart, or we get dragged about – I don’t see that.
“I see little key moments where we should be in their defensive third, and we don’t, and they [then] end up in our defensive third.
“I understand when you’re on the run that we’re in, but we have to find a way.”