After landing; the flight crew of a air carrier transport was instructed by ground control to 'follow two regional jets' toward parking. When those aircraft crossed the approach end of an active runway they followed. Ground Control advised they had not been cleared to cross.

Narrative

After exiting Rwy 9R at Taxiway N10 we were instructed by ATC to follow a Regional Jet westbound on Taxiway N and to hold short of Taxiway P. When approximately abeam Taxiway N5 we were told to follow another Regional Jet taxiing toward Taxiway N on N2. The First Officer acknowledged 'we will follow both'. ATC asked 'Verify that was (our flight number) who will follow the Regional Jet?'; to which the First Officer replied 'affirmative'. ATC responded (I paraphrase) 'I need to hear the call sign acknowledgment that (our flight number) will be following the Regional Jet'; to which the First Officer replied '(our flight number) acknowledges we will follow the Regional Jet'. By this time the Regional Jet was making the turn onto Taxiway P to cross the approach end of Rwy 9L. Per ATC instructions we followed the preceding Regional Jet. As we followed the Regional Jet onto Rwy 9L; ATC advised us to use caution because instructions to follow an aircraft do not constitute clearance to cross an active runway. ATC advised we had not been cleared to cross Rwy 9L. Within the context of this occurrence; ATC instructions to 'follow the Regional Jet' were quite definitive. The First Officer and I agreed to follow the Regional Jet; as instructed. Clearly; we are aware of all taxi procedures and should have asked for clarification from ATC. Taxi was expedited across the runway. Clear readbacks of all ATC communications with clear enunciation of call sign and vigilance for ambiguities or misunderstandings in communications; particularly where new or unusual procedures are in effect (e.g. use of approach end of ATL Rwy 9L as a 'bypass taxiway'); will largely prevent these occurrences.