Saints missed the chance to climb into second spot after old-boy Bradley Wright-Phillips cancelled out Radhi Jaidi's opener three minutes from time.
"We've got another point on the scorecard with 10 games to go," said Adkins.
"And I can speak from experience, having been promoted from this division twice, that there'll be plenty of twists and turns."
Charlton had lost seven of their previous eight games and Adkins admitted: "Chris Powell's players gave him everything and worked their socks off for him.
"It's early in his career and it's important he goes through some challenges but the players are having a right go for this club and I think they'll get through this sticky spell."
Source: PA
Source: PA