White, 23, was a virtual ever-present in Potter's rearguard last season as Brighton boasted the best defence record record of any team in the bottom half of the Premier League table.
White's £50m departure was confirmed yesterday but Potter insists Albion have plenty of competition for places in defensive areas and is not in a rush to spend the White money that has boosted Albion' s transfer kitty.
Lewis Dunk and Adam Webster didn't feature in today's 3-1 friendly win at Luton but will likely get some minutes in the final pre-season against La Liga outfit Getafe this Saturday.
Both players were excellent last season for Albion and will be a huge part of Potter's defensive plans this campaign that starts at Burnley on August 14.
Dan Burn, who hobbled off against Luton after his foot caught in the turf, will also have a big role to play as will Dutch international Joel Veltman, who looks the most natural replacement for White, who featured mainly on the right side of the defence.
Wing back Tariq Lamptey looks set to miss the start of the season but when he returns Veltman, who played mostly as a wing back last campaign, can drop back to fill void left by White. Poland international Jakub Moder is also more than capable at playing at right wing back.
Potter also has 21-year-old Norwegian defender Leo Ostigard, who impressed last season on loan at Coventry in the Championship, while the experienced Shane Duffy has featured in pre-season and looks highly motivated after a tough loan spell at Celtic last campaign.
Matt Clarke remains on the books but is on a season loan at West Brom.
Liverpool's Nat Phillips continues to be linked with Brighton but Potter is happy to be flexible with the options he has.
Head coach Potter said: “I think we have got enough competition in that area. We have got enough good players. We can be flexible with how we set up.
“You can’t replace a £50 million player, you have to look to be creative with solutions within the squad. But we are in a good place now.
“We wish Ben well, he has been fantastic. His journey from the academy to Newport County, to Peterborough, to Leeds United is fantastic for him. To then get a move to Arsenal is a great achievement for him and the club.
“It is a proud moment for everyone connected with the club and I am really pleased for Ben. The fee gives us a fantastic opportunity to develop the club and progress the team."
Potter was speaking after Albion’s first win of pre-season, a 3-1 victory against Luton Town at Kenilworth Road where goals from Aaron Connolly, Enock Mwepu and Percy Tau sealed a 3-1 win.
“I thought we played well in the first half especially; we controlled the game, created some good chances and scored some good goals. I was really pleased for Enock [Mwepu] to get off the mark.
“I am disappointed in their goal, which was from an error, and that made the start of the second half a little bit more competitive.
"It is something we just have to accept and learn from, but in the end our response was good and it was nice for Percy [Tau] to score the third.
“There were lots of young players on the pitch getting minutes towards the end of the game. It was a really good afternoon for us.”