Wendy Piatt also told a BBC Radio 4 documentary, broadcast this morning, that the shortfall could cost universities in the group around £80 million.
Several universities have struggled to meet targets for student recruitment this year in part due to the government's reforms allowing unlimited recruitment of undergraduates with A-level grades of AAB or above.
Dr Piatt told the Universities Challenged documentary, which charted the progress of the government's reforms to fees and funding: "Having far fewer students than planned does create a real financial hit.
"It's hard to give a very accurate number, but across the Russell Group it may amount to something like £80 million. We're not clear [on the final total] at the moment, but it's a significant amount of money."
The programme also featured an interview with Vince Cable, the business secretary, who said the AAB reforms were "experimental" and designed to try to free up existing "Stalinist" controls on undergraduate numbers.
Makers of the documentary were also given inside access to the University of Bedfordshire, whose former vice-chancellor Les Ebdon was at the centre of a political row over his appointment as the new director of fair access.