Before the game Mikel Arteta's side had gone seven Premier League games without a win, but Chelsea went 3-0 down before a late consolation from Tammy Abraham.
Blues boss Frank Lampard blasted his side as 'lazy' after their poor performance, who was angry with the way his side approached the game at the Emirates.
And winger Hudson-Odoi, who set up Abraham's goal, agreed with Lampard that his side started off on the wrong foot.
He said after the game: 'It feels like we let ourselves down. We know we can do much better. We should have put the same energy we had in the second half into the first half as well - we should have had the same attitude from the get-go.
'We started too slow, we all know that. We knew from the start it was going to be a difficult game no matter what. They're Arsenal, they're a good team.
'No matter where we are in the league we're going to keep pushing until we get to number one and no matter what the game is, we're Chelsea, we want to give our best every game no matter what.
'We don't like losing. That's the Chelsea mentality, we always want to win. So when we lose or make a couple of mistakes, we're all disappointed with ourselves. When we win we're always happy, when we lose we're disappointed, so we want to get back to winning ways and stay happy.'
Goals from Alexandre Lacazette, Granit Xhaka and Bukayo Saka had the game wrapped up at 3-0 after 56 minutes.
Chelsea grew into the game but Jorginho had a penalty saved by Bernd Leno and Abraham's goal came too late to trouble Arsenal, who won their first domestic game since November 1.
Lampard's side now find themselves down in seventh, six points off league leaders Liverpool, who have played one game fewer.
Next up Chelsea host Aston Villa on Monday 28, while Arsenal travel to Brighton the following day.
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