With City leading the game 2-1 the Wales international defender was dismissed for a second bookable offence 68 minutes into the game at Ashton Gate on Monday.
City failed to hang onto their lead with the visitors equalising four minutes into stoppage time to snatch a point.
"Lewin's tackle was unprofessional and I've spoken to him about it in the dressing room," Johnson said after the match.
"He's a good young player, but he has to learn from that mistake because it was the last thing we needed.
"Again we have let in a last-gasp equaliser and feel like we have lost, rather than drawn.
"I don't know what more we can do except to keep drilling the players on how to clear their lines.
"At the moment when the stoppage time board goes up it seems to create a siege mentality and we cannot hold onto the ball. It has cost us so many points this season and I'm more than frustrated by it."