Rovers were comfortable at half time thanks to a dominant performance and a goal from Mallik Wilks but became sloppy after the break and were pegged back by Scunthorpe who netted through Kyle Wootton.
Coppinger felt some of his team mates believed the game was already won and says they must realise where they went wrong at Glanford Park.
“I think it’s important they realise what actually happened,” Coppinger said.
“They've been amazing this season in situations like this, in games where we’ve had to dig in, in so many different circumstances.
“This was another one where you got lured into a false sense of security. You think you’ve won the game, it’s easy.
“We were getting opportunities and breaking on them.
“Before you know it, you’re at 1-1 and it’s harder to get back in the game then.
“I think the hard work needs to be done at 1-0 to get 2-0 or 3-0 up, when you’ve got the opportunity.”
The veteran forward says the focus must be on killing games off in scoreline terms, no matter how comfortable the side is in performance terms.
And he said the lessons from Glanford Park must be taken forward as Rovers look to cement their place in League One’s top six.
“As soon as we bypassed their midfield and got onto their back four, we never took advantage of that,” Coppinger said.
“I thought we took too many touches on the ball and maybe thought it was too easy.
“We’ve got a few young players that are learning all the time.
“You have to kill games off and we didn’t do that.
“That is why the gaffer will be disappointed and why we’re disappointed.
“It was a big opportunity for us but we’ll have more opportunities.
“If we learn from it we’ll go into the next 14 games and if we get into this position again we’ll be able to deal with it better.”
Rovers boss Grant McCann confirmed striker Wilks was withdrawn in the second half due to a deadleg.