Losing Declan Rice makes Brighton players more free to play more openly because Arsenal are one man short.
But even so, Arsenal still kept up the game and it's just that they were unable to create opportunities to score a second goal.
Next Arsenal will visit Tottenham's headquarters and if they don't want to experience the same thing, Arsenal must play carefully so as not to lose points like when facing Brighton.
Tottenham will definitely not let Arsenal get full points and my prediction is that the match will end in a draw.
Arsenal will still aim for full points at Tottenham's headquarters in the next match even though Tottenham will try not to give Arsenal full points in that match. Because the quality of the players owned by Arsenal is still slightly better than that owned by Tottenham this season, so I am not sure that their match can end in a draw again like when Arsenal hosted Brighton last weekend. In addition, what you said about having to play more carefully can also be applied by Arsenal because they are currently hunting for a win in order to immediately achieve a better position like what Manchester City and Liverpool have achieved at the start of this season.