Antonio Conte praised his players for their never-say-die spirit but admitted he was hugely relieved to reach the Carabao Cup semi final.
Chelsea supersub Alvaro Morata got an injury time winner less than a minute after Bournemouth midfielder Dan Gosling’s equaliser appeared to have taken the tie into extra time.
Morata could not contain his joy celebrating and was booked by referee Lee Mason which now rules him out of Chelsea’s trip to Everton on Saturday.
Chelsea boss Conte, whose side now faces Arsenal in the semi final, said: “We must be pleased. We had a great reaction to their goal.
“It’s not simple conceding a goal in the last minute of the game, but when you have this reaction you have players with great character, personality and talent. We must be pleased.
“I’m very happy. Very happy for the performance of these players, because it means we are working very well.
“But I must be honest, I didn’t see this yellow card. He’s a big loss for us, especially because we have to play a tough game against Everton.
Bournemouth boss Eddie Howe said: “It feels heartbreaking, to be honest.
The players gave everything to get back into that game. Second half we penned them in with a wave of attacks, scored a great goal.
“I was hoping it would go into extra-time and we’d have a go at winning it. It was bitterly disappointing what happened in those last few moments. The majority of that back-line are experienced – it’s too painful to watch the goal again – so I don’t think they switched off.”