Livermore netted with a 25-yard screamer and put in a man-of-the-match display to inspire the Baggies to a 1-0 win at Hull on Saturday.
It was the latest in a string of impressive performances from the 29-year-old who has formed an excellent partnership with Romaine Sawyers in central midfield.
The only downside to Livermore’s display was that he picked up a fifth yellow card, meaning he will now miss the game against Sheffield Wednesday – with Sawyers also set to miss the game having also picked up five bookings.
Bilic, though, had nothing but praise for his skipper.
“Jake has been fantastic from the first game,” the head coach said.
“He likes to pass, he’s a captain, he’s a leader.
“He’s a top professional, a top player, and it’s a privilege for me as a manager to have him on the pitch.
“It’s not a chance when you receive the ball 25 yards from goal but his strike was magnificent.
“Not only that, his whole performance, it was a proper captain’s performance.
“It’s just a shame he got the fifth yellow, and Romaine also, so it’s good at least that we have some time now to think about what we’re going to do for Sheffield Wednesday.”
As well as being impressed with Livermore, Bilic was also pleased with how Hal Robson-Kanu led the line in Yorkshire.
After a number of impressive cameos from the bench, the striker was restored to the starting line-up at the expense of Charlie Austin.
And Bilic felt the Welshman was integral to his side’s victory.
“I was very impressed with Hal,” the head coach continued. “The work-rate, but the work-rate is not enough. That’s a minimum.
“The way he kept the ball, his skill and technique, the way he brought other players into the game, was magnificent.
“The wingers are Hull’s best players so we didn’t want to leave our full-backs one against one with (Kamil) Grosicki and (Jarrod) Bowen.
“That required our wingers Matt (Phillips), Grady (Diangana), Kyle (Edwards) when he came on and Matheus (Pereira), to go really deep.
“For that, you need somebody to get the ball and hold the ball for a couple of seconds until they join. Hal was instrumental in that for us.”