Arsenal have now suffered four successive defeats in all competitions, and Sidwell has criticised the Gunners for playing with "no passion" during the Premier League encounter on the south coast.
The 35-year-old told talkSPORT: "It is what everyone has been saying of late - there are no characters, no fight, no desire, no passion to wear the shirt and that was evident yesterday.
"Before the game I saw them in the tunnel and their body language wasn't that of a team that was ready to roll their sleeves up and give it a go. We knew from the off, if we had a good start and played on the front foot and got after them, we would have a chance.
"All it seems they have got is their flair and technical ability - and that has even gone now. Their confidence is shot to pieces."
Brighton now sit in 10th position in the Premier League table, just 11 points behind sixth-placed Arsenal.