Luiz was shown a straight red card late on for a poor challenge on Sead Kolasinac which saw both benches rise to their feet.
The Brazil defender, who had earlier been booked for catching Laurent Koscielny with an overhead kick, now faces a three-match suspension which would include the Premier League visit of Manchester City.
Conte reckons Luiz was fouled by Alexis Sanchez prior to the challenge which saw him dismissed three minutes from time.
Conte said: "It's very important to see what happened before the David Luiz tackle. For sure there was a foul.
Chelsea may yet appeal against the length of the suspension, which will also see Luiz miss Wednesday's Carabao Cup clash with Nottingham Forest and next Saturday's league trip to Stoke.
The Blues have now received five red cards in their last eight games, including May's FA Cup final loss to Arsenal, with four of those this season.
Conte said Chelsea must work on their disciplinary record, like other aspects of the game, and require more good fortune - in avoiding dismissals and in opponents being sent off.
The Italian said: "I hope to be more lucky with the referee's decision, for us and also for the opponent.
The Gunners had the better chances, the best when Alexandre Lacazette shot wide after Aaron Ramsey had hit the post, while Shkodran Mustafi had a goal ruled out correctly for offside.