Liverpool goalkeeper Alisson scored header in stoppage time to secure a 2-1 victory and boost the Reds' hopes of securing Champions League football.
Speaking in his post-match press conference, Allardyce said: "You know Jurgen, he always thinks he's right doesn't he? He's always right so maybe I am today.
"He's a lucky man tonight and he knows it."
Allardyce said: 'There's no way with Matt Phillips in front of the goalie or not that goalkeeper would have saved that ball (Bartley's disallowed goal).'