On what was a disappointing trip to the North East, the Magpies went ahead after just 23 seconds when some poor defending from Branislav Ivanvoic led to Miguel Almiron firing in.
After a disappointing first-half display, the Baggies improved significantly after the break but former loanees Jacob Murphy and Dwight Gayle combined to produce a moment of brilliance to earn the points for Steve Bruce’s side.
The result means Albion have now won just one of their last 16 league games - increasing the pressure on head coach Bilic.
But when asked about his future, the boss insisted his team showed enough character at St James’ Park to give them a fighting chance of avoiding relegation this season.
“It’s not a question for me,” Bilic said when quizzed on his future.
“I am doing my job, I haven’t detected any signals, I haven’t had any talks.
“I prepared for this game and that is all I can say. I am doing my job.
“And today we showed, it’s about the result of course, but we showed again that we are in games until the end.
“We showed a character, a mentality, a quality up to a point. The team is very much alive.”
Bilic felt, overall, there was very little to separate the two sides with the difference in the end Newcastle’s quality up front.
“It was fine margins again,” the head coach continued.
“We have to admit it was a game of two halves.
“In the first-half they scored very early from a situation where basically you have to do better.
“After that it was their quality up front that was better than ours and they got into a few dangerous situations. They were much stronger in the first-half.
“Second-half we made some changes but it was more our change in mentality, in bravery, that made a difference.
“We were good. We scored a goal and we were getting into situations in the final third - in those pockets.
“We weren’t just playing in front of them or wide and you expect - when you break those lines - to create clear cut chances. But we didn’t do enough of that.
“And then we conceded a goal that we know how to stop.
“You can talk about a really good cross and a brilliant finish but we have to stop it and when the cross comes you still have three centre-backs who should cope with that ball better.
“Again it’s very frustrating. It was fine margins but it went to the opponent and we are again going home empty handed.
“That is very frustrating because I think we deserved something from that game.”