The message fell on deaf ears. Besides Crusher and Picard, the rest of them kept bickering afterward. It was only the Romulan that messaged Picard afterward acknowledging the general point of the message saying "Perhaps were not completely dissimilar.." .
The Klingon and Cardassians quickly left orbit, probably forgetting what that message was about and returning to their home worlds. Probably the contents of the message was stored away by the Federation and Romulans in some database somewhere.