The 2-1 defeat, having taken the lead through the 40-year-old in the 13th minute, was Rovers' ninth in 14 games, only two of which have been won – a sequence stretching back into the latter days of previous manager Darren Moore's reign.
From being well placed for automatic promotion thanks to their games in hand at the start of the run, they are now tenth, five points behind Lincoln City, who are in the final play-off spot and have as many matches remaining.
Coppinger, who has scored twice in his last four matches, was angry with the Easter Monday performance at the Memorial Ground against opponents who even now are in the League One relegation zone.
“Just not good enough individually, collectively,” he said. “We got off to a good start, got the goal, and then we stopped doing what we'd been doing up to that point. It just amazes me.
“Ten games to go, we were in such a good position, so to come away with a defeat is tough to take.
“Individually we have to take responsibility, look at ourselves and do better.
“Bar a couple here and there, we're just not good enough as individuals. We were absolutely miles off it.
“From the start of the game to when we got the goal I thought we played really well and cut them open. After that we just stopped doing what we should have been doing all game.”
Moore's departure for Sheffield Wednesday, plus that of head of recruitment Adam Henshall to Aston Villa, and the January sale of captain Ben Whiteman to Preston North End have all disrupted the club but Coppinger says the main problem is players are simply not playing well enough or even showing the commitment needed.
“We need to change individually, to take ownership and responsibility for what we're doing on the pitch,” said the Teessider, who retires at the end of the season. “You can speak about the manager (Andy Butler) or formations but ultimately it's down to how hard you want to work, how motivated you are to get to the next level and for me, you look at it on the pitch and you can't see it.
“It's hurting because I'm retiring at the end of the season and I know what it takes. They (Bristol Rovers) wanted it more than us and we should want it as much as them to get into the play-offs.
“I've got nine games left and I'll put everything into those nine games and see where it takes me but it needs to be better. We've got to look in the mirror and sort ourselves out first. You have to know what you're doing, want it and do the basics and we didn't do that.”
Doncaster are at home to one-from-bottom Wigan Athletic on Saturday.
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