The Merseyside outfit were heading for a comfortable win at St. Mary's Stadium when the new arrival passed the ball straight to former Reds striker Danny Ings at close range in the 83rd minute.
Per Goal's Chris Burton, Wijnaldum said:
"Those kind of things can happen with a goalkeeper.
"Last season it happened to Alisson against Leicester City and in a pre-season friendly.
"How is he [Adrian] going to react to the mistake? I think that is more important than the mistake itself.
"Everyone can make a mistake, also a goalkeeper. But the only thing is, he is a goalkeeper, and if he makes a mistake, a lot of times, it will result in a goal."
Adrian joined Liverpool on a free transfer this summer after being released by West Ham United.
He was thrown into action after No. 1 Alisson suffered a calf injury against Norwich City in the opening match of the season.
The Spaniard saved a penalty from Chelsea's Tammy Abraham in a shootout victory in the UEFA Super Cup on Wednesday, but on Saturday his error set up a nervy finish for Liverpool.
Like Wijnaldum, Liverpool writers Scott Groom and Joel Rabinowitz compared Adrian's mistake to one made by Alisson against Leicester early last season:
In that match, the Reds were also 2-0 up when Alisson was caught on the ball by Kelechi Iheanacho, allowing Rachid Ghezzal to pull one back for the Foxes.
The Brazilian was able to put the error behind him, though, and his superb goalkeeping played a key role in Liverpool conceding just 22 Premier League goals last season, the best record in the division.
Adrian isn't on the same level as Alisson, so mistakes will be more common as long as he's between the sticks instead of the No. 1.
It's still early in his Liverpool career, though, and if he can limit the number of such incidents until Alisson returns he can keep the Reds competitive in the meantime.