With just seven matches remaining, Irish sit just one point off the bottom of the table, but Fisher has claimed that they can escape.
"In recent weeks we've been playing well so we won't be hitting the panic button," Fisher told BBC Sport.
"It's an uncomfortable position to be in, but we cannot worry about other teams. We need to focus on ourselves. We need to play with the same intensity that we have done against the likes of Saracens and Gloucester."
Irish were beaten 40-16 by Bath Rugby in their last league clash.