Posh were already trailing to Paul Anderson's goal when Tomlin was sent-off for felling City defender Greg Cunningham with an outstretched arm.
Grant McCann levelled for Ferguson's men soon after but they were well out of the game, with some poor defending creeping back in to their play, by the time Dwight Gayle scored a late consolation to continue his scoring run.
"I'm not going to blame the sending-off of Lee for our defeat. We cannot start games as poorly as that and expect to get anything," Ferguson said.
"I don't think Lee intentionally used his elbow on an opponent, but if you raise an arm you take a risk and we will now lose him for three games.
"That is a big blow because he has been in good form. But Bristol started really brightly and it was the goals we conceded, rather than the red card, which cost us.
"The two in the second half were soft and put us out of the game. We must now brush ourselves down quickly for a really big game against Barnsley."