Blues boss Antonio Conte paired Morata with Olivier Giroud in a rare front two for Chelsea and the duo made life difficult for Sean Dyche's side, whose five-game winning streak came to an end.
Morata missed a one-on-one - replays indicating goalkeeper Nick Pope may have touched the ball wide of the post - and was evidently highly frustrated on his withdrawal, kicking out at the dugout and throwing his boots and shinpads to the ground in disgust.
And the Spain international tweeted after the match to express his regret at that reaction.
He wrote: "Three important points for us. The best way to get ready for Sunday’s game was winning today.
"I want to apologize for my reaction when I was sent to the bench, when I fail I get really angry with myself."
Three important points for us. The best way to get ready for Sunday’s game was winning today. I want to apologize for my reaction when I was sent to the bench, when I fail I get really angry with myself. pic.twitter.com/Vxg4eC7X3Q— Álvaro Morata (@AlvaroMorata) April 19, 2018
Conte, though, says he understood why Morata - who has only scored once in the Premier League in 2018 - was annoyed.
"Alvaro must be angry, because when you have the chance to score you have to score and it can change your confidence," he told a post-match news conference.
"He was angry with himself for his missed chance. But I have to see his whole performance and it wasn't possible in the past to play with two strikers. They did a great job, as did the whole team.
"Around 70 minutes I thought that it was better to use fresh strength with Hazard. He is a player that has different characteristics to Morata. I am pleased for their performances, they played very well."
But with only four matches of the season remaining, Conte believes it will be difficult for Chelsea to chase down their London rivals.
"I'm not sure. The only way to keep a hope from now until the end," he said of Chelsea's top four hopes.
"It won't be easy. There is a gap of five points with Spurs. If we think in the past we have missed great chances to get closer to them. Now we have to get three points every game."