The hosts took the lead through Pulisic in the first half but went down to 10 men moments later when Thiago Silva picked up a second yellow card before 30 minutes.
Mason Mount reduced the deficit late on, but the result dents Chelsea's top four hopes this season.
"We gave away two very easy goals. What could go wrong went wrong after the red card," Tuchel told BT Sport after the game. "We have to accept the big loss.
"We did big mistakes before the two yellow cards. There were too many easy ball losses. It was impossible for us to accept the situation. Every shot was a goal from them.
"Clearly it was not our day today. We will get the right response. First of all it's important we digest it. I did not see it coming; now we have to take our responsibilities -- me included -- and shake it off."
Less than a minute later, Silva was sent off for a late challenge on Okay Yokuslu and the visitors went ahead before the break with a quickfire double from Pereira.
Robinson finished off a well-worked team goal after the hour mark, and Diagne grabbed a fourth moments later.
Chelsea hit back three minutes later when substitute Mount scored, but Robinson notched his second in stoppage time to secure a stunning victory for West Brom.
Pulisic appeared to pick up an injury that forced him to come off at half-time. He initially entered the pitch alongside his teammates for the start of the second half, only to turn around and speak to his manager before coming off.
Chelsea remain in fourth place, while West Brom stay in 19th place and seven points from safety.
"It was a tough first half for us. We made some simple mistakes we don't normally make," Pulisic told BT Sport. "The red card changes everything. To give them credit, they played their attacks really well. It's no time to panic. We've been in good form and lost one game. We need to be ready for midweek."
West Brom boss Sam Allardyce told BBC: "I am delighted. Not only with the win but the style; it has been coming for a while, but our lack of finishing has cost us.
"What we saw today is what we have been missing. The quality of our goals and our football brought us a fantastic result. We were desperate for it. They went down to 10 men, deservedly so. Thiago Silva could have gone for his first foul. But on many occasions I have got a result with 10 men, but we took Chelsea apart."