Such statements are admissible in court. A suspect's spontaneous statement linking himself to the attack, and containing information he could not know unless he participated in the attack, can be very damning evidence. It may not be physical or forensic evidence like we are used to seeing on CSI and similar TV shows, but it is certainly admissible and compelling evidence.

Plenty enough to support a jury finding guilt beyond a reasonable doubt, even in the absence of DNA or other physical evidence.