Bournemouth took full advantage and, after Jordan Ibe hit a post, equalised for the second time after a protracted scramble in the area from another corner.
"That was just one of the few good opportunities that we had, in what was a fairly open game at times".
Anthony Knockaert and Glenn Murray were on target as the Seagulls took the lead twice although they were pegged back on both occasions, with Steve Cook heading home before Wilson's point-earning strike on 79 minutes.
"We make it hard for ourselves and that's where true character comes though".
Brighton's FA Cup fixture is against Crystal Palace next Monday.
BC-SOC-Brighton-Bournemouth, 2nd Ld-Writethru, 152 Knockaert scores 1st Premier League goal in 2018AP Photo LON813, LON829, LON824, LON810, LON812, LON815Eds: Adds detail in fourth paragraph.
He prevented the home side from killing the game off by denying Murray with a fingertip save as well as clearing two close-range efforts from Izquierdo.
Chris Hughton's side had the better of the play, with more possession and more shots on target on the day, but were unable to get one past Newcastle goalkeeper Karl Darlow. At some point though these rescue acts are likely not to come off, and then you worry for the Cherries. "It can alleviate the pressure".
However, although Brighton keeper Matt Ryan had to make good saves from Isaac Hayden and Dwight Gayle, the technically superior visitors enjoyed the better of the game and might have emerged with more than a point had Karl Darlow not managed to repel Lewis Dunk's 68th-minute header.
"The timing and the manner we conceded was disappointing".
Bournemouth will go for the double over Brighton, having already beaten the Gulls in the reverse fixture by a 2-1 score at Vitality Stadium in September.