Barca were heavily linked with a move for Depay following the arrival of new head coach Ronald Koeman, who allowed striker Luis Suarez to leave for Atletico Madrid.
The Netherlands international had agreed terms with the Catalan giants but a deal between the clubs could not be reached for the transfer deadline on Monday.
Depay's contract with Lyon is due to expire in June and he hopes by continuing to impress with the Ligue 1 side he can still secure a move to Barca.
Asked about the prospective move following Netherlands' 1-0 friendly loss to Mexico on Wednesday, Depay told NOS: "It was pretty close.
"We don't need to go into all the details, but there were certain rules that prevented it unfortunately.
"But I believe everything happens for a reason. I now focus on Lyon and want to be important there again.
"We'll see how things are going again afterwards. If I do my thing, the interest may still be there. I just have to switch that switch now."
Depay joined Lyon from Manchester United in January 2017 and has been involved in 79 goals (47 scored, 32 assisted) in 107 Ligue 1 games – Edinson Cavani (83) and Kylian Mbappe (89) are the only players to have had a hand in more since the weekend of the Dutchman's debut.
In addition, Depay has created 259 chances for team-mates in league matches with Lyon, with Dimitri Payet (338) the only player to have supplied more key passes.