Herbst came back on approximately three minutes earlier than expected and was involved in a crucial tackle that helped the Harlequins to win 40-36 in a thrilling game where Bath were down 40-3 at one stage.
The RFU said in a statement on Sunday that its Professional Game Match Officials Team (PGMOT) had acknowledged the mistake.
"We would like to apologise to both teams for this mistake. As is the usual process the PGMOT will review all games to ensure continued improvement and learnings."
However, Bath will feel aggrieved after the RFU said the result of the match remained final.
"I flagged it with the referee after the game," Bath's director of rugby Johann van Graan said.
"There's not a lot that he can do, on the pitch he wasn't even aware of it. We went through our team manager and we made the fourth official aware. On a yellow card, you're supposed to be off for 10 minutes, not seven."
