Williams came up through the youth ranks at Liverpool and remained on the books at the club until last summer, when he was sold to Nottingham Forest.
He scored Forest’s first goal in their 3-2 loss away at Liverpool, but did not celebrate due to his past lengthy association with the Anfield outfit.
Thompson believes that Williams was wrong to have a mooted celebration though and should have taken the opportunity, especially as he is not likely to score many goals.
“You’ve left the football club, you’re being employed by someone else, I don’t care who you are or what club that you’ve gone to, celebrate the goal”, Thompson said after the game on LFC TV.
“Particularly for a right-back, they don’t come along too often.
“I can’t fathom out that, not celebrating.”
Nottingham Forest remain deep in trouble in the Premier League and have a tough run of fixtures on the agenda as they look to save themselves.
They are next due to play host to Brighton at the City Ground.