The diminutive winger dropped to the bench for the first time this season after boss Russell Slade handed a debut to Nottingham Forest loanee Arron Davies against Wycombe.
But Cox came on as a substitute and set up Nicky Forster's 75th-minute winner as the Seagulls grabbed their first victory of the campaign.
"There's competition but it's not a problem. It's always healthy," he said.
"Hopefully I've put in a decent 20 minutes or so to try to get myself into the team for Saturday."