Rovers survived 50 minutes with 10 men in what could prove a critical game near the foot of the second tier.
They may only have earned a draw, but it was good enough to take them a point and three places clear of the drop zone with two games to go.
“Obviously with a man getting sent off it was hard for us, but what a performance from everybody,” said Coppinger, following the 40th-minute dismissal of Abdoulaye Meite.
“To come away with a point after the disappointment of going down to 10 men, we’re delighted.”
Doncaster had lost four straight going into the pivotal game at the New Den, but Coppinger insists the result has strengthened their belief that they can stay up, with games to come against play-off hopefuls Reading and champions-elect Leicester City.
Coppinger said: “The last four games we haven’t been getting the results that we need, but everybody’s working hard and doing the right things and at this stage of the season that’s what you need – no one is shirking responsibility.
“Considering the circumstances, Monday was massive and to get a result at this stage of the season could be the difference in staying up. I think it’s galvanised the team.”
Barnsley, who are four points adrift of safety, have recalled striker Danny Rose from a productive loan spell at Bury.
Rose, 20, scored three goals in six appearances for David Flitcroft’s Shakers, the same record as Barnsley have managed in that time.