Liverpool conceded their 12th goal from a set-piece during Saturday's 2-1 victory over Wolverhampton Wanderers, the joint-most in the Premier League alongside Bournemouth and Nottingham Forest.
The champions rarely threaten from set-pieces at the other end either, scoring three goals from dead-ball situations, excluding penalties, this season, nine fewer than leaders Arsenal. Their non-penalty set-piece difference of minus-nine is the worst in the league.
"We've conceded too many set-piece goals, and we don't score enough," their captain, Virgil van Dijk, said on Sunday.
"It's something we have to improve. I would say at least 75% of the time, or even more, it's not even about the first contact.
"It's the second phase that is the killer. Is it a mental thing? I hope not. If that's in your head, then it's an issue."
Briggs joined the club in September. Responsibility for set-piece preparation will now be shared by the rest of the coaching staff.