The incident occurred a little more than five minutes into the third period during the Canucks' 5-1 victory against the Predators at Rogers Arena. Weber was assessed a minor penalty for boarding Vancouver's Jannik Hansen behind the Nashville net and another two minutes for unsportsmanlike conduct.
"On all plays we deem to be illegal there are varying degrees that escalate from one level to the next," Shanahan said. "I didn't like this hit, and I expressed that to Shea Weber. I feel it was an illegal hit. I would like to see less force in that situation and that is why he's being fined. He didn't use all of his force, and did get Hansen sort of on the right side of Hansen's body -- I think a lot of Weber's impact and the sound was him hitting the glass. It wasn't square in the numbers, but it was illegal."
Weber has played 408 games in his seven-year NHL career. He finished last season 19th in the League with 211 hits, which was sixth among defensemen.
Another of the League's top defensemen, Pittsburgh's Kris Letang, was suspended for two games earlier this week after an illegal hit on Winnipeg's Alexander Burmistrov.
"The big thing for me is a player's history," Shanahan said. "That to me is something I've done so far. If you see my highest suspensions, it is when there are multiple offenses. Weber has played a long time in the NHL and played a very physical style and had no offenses. Also, there was no injury on the play.
"It is a situation where he can't make that hit that way again. He's now in a situation similar to Letang where he has a fine on his record. Letang's fine is a significant reason why he got suspended instead of fined."
For our team, as a group, we've never been this far before, and so it's just more lessons learned, and sometimes you have to go to the school of hard knocks to find out what works and what doesn't. We've got a young group. They've played some unreal hockey here to get us this far, and we showed if we're not going to play the proper way, a really, really good hockey team is going to beat you, and that's what they did. It's a lesson learned.
— Lightning coach Jon Cooper after Rangers win in Game 6 forced a Game 7 that will be played at Madison Square Garden on Friday