Morata and Loftus-Cheek have found the going difficult under Sarri, despite Chelsea’s undefeated start to the Premier League season , with the former struggling for form and the latter for starts.
However, Loftus-Cheek made the most of his chance in the Europa League, scoring a hat-trick against BATE in midweek , and though he did not grab his first Premier League start of the season in the 4-0 win over Burnley, he did add a goal off the bench.
Meanwhile, the heavily-criticised Morata picked up his third goal of the Premier League season to open the scoring, while Ross Barkley and Willian added the other scores for Chelsea, who were without Eden Hazard in the win.
However, Giroud, who came on for Morata in the 74th minute, could not do the same and remains without a goal in all competitions for the Blues this season.
Sarri was left pleased with Morata and Loftus-Cheek after the victory, but admitted that he believed the France international could have found the back of the net as well.
"For 10 minutes it was difficult at the beginning but then we played very well. I am very happy for Alvaro Morata and Loftus-Cheek again,” Sarri told reporters.
“I am disappointed for Giroud because today I thought he could score. He needs to score.
"At the end, everything is OK. We played very well in full control of the match for the last 80 minutes.”
Sarri spoke further on Morata, who he admitted probably could have added another goal to his tally, but hopes that his recent performances can be a springboard toward something greater.
"I think that Alvaro today played well," Sarri said. "He went to the ball when it was necessary. I think he played a very good game. He probably could have scored more as he had three or four opportunities, but he scored a good goal.
"I think the last three or four matches can be a good start for him."
The win moves Chelsea up to second in the Premier League table ahead of Manchester City's match against Tottenham on Monday, but the next challenge for the Blues will come on Wednesday in the Carabao Cup against former Blues star Frank Lampard’s Derby County side.
And Sarri is already turning his focus toward that midweek cup clash, noting he expects a real challenge for Chelsea to advance to the next round.
"At the moment we have to start to think about the next match,” Sarri added. “We play on Wednesday and we have a difficult game, we want to go on in the competition."