The draw with Shrewsbury on Saturday means that Colchester only need to take a point at Carlisle United to secure safety and send Scunthorpe into the basement division.
But Dunne was furious with how his team, who were booed off the field, performed against the Salop.
“It’s a big week where you can either be a League Two player and disappear or a League One player and push on," he said.
"We are staring relegation in the face.
“Now it comes down to the last game at Carlisle, which isn’t in our advantage.
“We have to regroup, turn up and give a better account because there are a lot of jobs on the line"