Regan was cited for kicking Gloucester's Luke Narraway in Bristol's 14-12 victory on November 24.
With David Blaney (rib cartilage) and Neil Clark (knee) already sidelined, any period of suspension would have left Saul Nelson as Bristol's only recognised hooking specialist for Saturday's European Challenge Cup clash at Bayonne.
Although the kicking charge was upheld, the RFU's disciplinary panel ruled no further punishment was necessary.
London Irish will be without French flanker Olivier Magne for this weekend's Heineken Cup appointment with Ulster, after he was given a two-week suspension for stamping on Northampton's Dylan Hartley.
The ban dates back to November 29 when Magne was suspended by his club - and means he will be available for the return game against Ulster at Ravenhill on December 15.