The result lifted Eddie Howe's men above Grimsby and has raised hopes of beating the drop but Pearce is refusing to get carried away.
"There were no big celebrations because we know we have to focus on the Port Vale game," he said.
"That is the latest cup final for us now and we have to keep pushing on and keep putting in good performances.
"It's a massive boost to get out of the bottom two, but it's a different kind of pressure now. It has been so hard mentally and physically to get where we are now, but now we have done it, we must push on."