The former Albion right-back and academy coach was targeted for X-rated abuse from away fans as their side were swept aside 3-0.
His dismissal was confirmed on Wednesday afternoon, less than 24 hours after the game.
It was their fifth successive defeat and they have not scored a goal in that time.
Chelsea were out-played and out-thought by Fabian Hurzeler’s side and should probably have lost by a heavier margin.
Rosenior, a popular and respected figure among Albion players, staff and fans during his time at the club, looked an angry man after the game.
He spoke to broadcast media and in his press conference about a performance which was not acceptable.
Callum McFarlane will take charge until the end of the season, starting with Sunday’s FA Cup semi-final against Leeds.
Defeat for Chelsea would have a knock-on effect for Albion as it would mean a rescheduling of their late-season Prem trip to Elland Road.
Rosenior told reporters at the Amex: “The buck stops with me. I have thick skin and I understand why the fans are frustrated.
“I’m frustrated with the performances we’re putting in. I’ve just got to keep working hard with the staff, with the players.
“But what I do need to do is really look at how we go about games, the personnel of the team, who I can trust and rely on in difficult moments, because not enough players showed that.”