A door latch system includes an exit device having a housing mounted to an unsecured side of a door. A latch assembly is mounted in the housing and includes a latch for releasably securing the door in a door frame. An actuating assembly includes a driving member. A push bar is configured to be received within the housing. Relative movement between the push bar and base plate so as to reduce the distance between the push bar and base plate moves the driving member and latch to release the door from the door frame. A dashpot is connected to the driving member and configured to allow movement of the driving member when the push bar is manually depressed but to resist movement of the driving member when a secure side of the door experiences a high velocity impact. A method of resisting unwanted unlatching of the latch is also disclosed.