Webb went across to the technical area and dismissed Megson who spent four-and-a-half years in charge of the Baggies.
It completed an afternoon of mixed emotions for Megson who was "humbled" by the reception he received from the Albion fans but frustrated at his side's inability to secure a first away win for four months.
Megson said: "I quite rightly got sent off for getting the a*** with the referee. I told the linesman three or four minutes beforehand that we wanted to get Ebi Smolarek on the pitch at the next break in play.
"As soon as the ball went out I thought 'here we go' and they took the throw and carried on and I just got the hump and got myself sent off.
"I have apologised to Howard Webb. I shouldn't be like that but you get carried away."
Matt Taylor gave Bolton the lead with his eighth goal of the season before an own goal from Danny Shittu salvaged a point for the bottom-placed Baggies.
Megson said: "I am not pleased with a point. I thought we were well on top.
"I can't remember them having a shot on target. I thought even the goal was a shot which was going wide until it hit Danny Shittu on the thigh.
"Scott Carson has made two fantastic saves, the one in the first half from Kevin Davies' header and the one at the end from Matt Taylor, has probably let them live to fight another day.
"We needed to respond to the way they played against Fulham and we did that."
Regarding the reception from the home fans, Megson said: "It was humbling because I didn't expect it because I know what they are like and they support the team.
"When I arrived here, they had been supporting the team through thin and even thinner times and we managed to get it going, pick it up a bit and they were great with me.
"The reception I got was humbling and it was difficult to deal with and I appreciate it."
Albion manager Tony Mowbray insisted his side would not throw in the towel in the bid to stay in the top-flight despite another setback to their survival hopes.
He said: "These are the sort of games we were hoping to win. We didn't. We are disappointed. But what do you want me to say - 'Yes, it's over' or 'No, it's not over'?
"We play the next game. It is against Stoke. We are disappointed today. It was a strange game. They probably had more threatening moments in the game through the way they play.
"Yet, I felt for long spells we controlled the game. We went a bit cavalier at the back after taking the two full-backs off and we nearly got the win but it wasn't quite to be.
"I've never questioned the players in terms of them giving up the ghost. You tell me if you think they are giving up the ghost. I don't think so.
"I think they understand it becomes more difficult but they have got to keep applying themselves. I only asked them to play in the way we set the team up to play and keep going. I enjoy watching my team play.
"Great credit should go to the players for having a go in the last 20 minutes after we had gone behind. We got back in it and nearly won it.
"I would rather gamble to lose a football match trying to win it."