The stalemate at Stamford Bridge was a good point for lowly Brighton who are now seven points above 18th placed Fulham with a match in hand.
Brighton created the better chances and were unlucky not to take all three points as Adam Lallana fired a shot just wide when well placed and Danny Welbeck cracked the post with an excellent curling effort from the edge of the box.
The only down side for Albion was the second yellow card White picked up in the dying minutes - just moments after he was given the man of the match award.
White received his first booking as he left a boot in on Mason Mount and was then given his marching orders in injury time for hacking Reece James as the Chelsea man made good progress down the left.
Potter said: "I did not clearly see the first yellow. Then (the second yellow) we are caught up the pitch with a turn over.
"I think it was a one v one situation and he makes a challenge and I think it is a yellow card. So we will have to adapt and deal with that."
Brighton midfielder Lallana, who came on as a second half substitute, thought Albion fully deserved the point but was disappointed he didn't convert his golden opportunity. "We had a couple of chances at the end. I should have buried mine.
"That is what football is about - the underdogs coming here tonight. We were outstanding and should have taken three points.
"Huge positive again, like all season. We will keep plugging away and get more points on the board. We have a world class manager and good players, The lads are taking his instructions on board. We believe we are going to get points at big clubs."
On the European Super League, the former Liverpool midfielder added: "It is surreal. I was saying to one of the other lads I had this funny feeling all day.
"When we heard teams had pulled out it went away. I am not sure what has happened during the game.
"What has been shown is that together we are stronger than anything. It is great to see everyone coming together as one. We want games like this to have meaning.
"We are fighting for our lives, Chelsea are going for the Champions League."