The £6million deadline-day signing from Everton finally ended his goal drought on his ninth appearance for the Baggies, scoring in the fourth minute of injury time in a 3-2 defeat at home to Manchester City..
Anichebe's failure to find the net has meant the 25-year-old has not started a game since a 4-1 defeat at Liverpool on October 26.
The Nigeria international, however, is relaxed about his opportunities as he continues to settle in at his new club.
"Longy (Shane Long) has played really well, so has Sess (Stephane Sessegnon). He scored some great goals against Villa and Chelsea," said Anichebe.
"If someone is playing well then sometimes you have to wait for your chance.
"I was playing well after Man United (a 2-1 win on September 28), but I've had a few niggling injuries since then which knocks you off your feet for a couple of games.
"If someone then comes in and plays well, fair play to them. I'm the first to congratulate anyone who is doing well.
"But I don't get frustrated. If I play I play, if I don't I don't. I'm not one of those people who is going to start fighting the world.
"I will simply do my best and if that's not good enough, I will wait my turn. I'll just keep working hard and we'll see where that gets me."
Anichebe was at least relieved to get off the mark, even if it came at the end of a game in which Albion were second best for most of it.
"I always knew sooner or later a goal would come, and I'm delighted, but it's difficult to take because we lost the game," he added.
"But it is really important (to score). In my first game for Albion at Fulham I should have scored then.
"I was really disappointed because nine times out of 10 I'd have scored, and I didn't.
"But when you're always in and out and you get a niggle here and there it disrupts you, especially when you come to a new club and new surroundings.
"It takes time to get used to everything and I'm still doing it."
Without a win now for four matches and after back-to-back defeats in the space of five days, the overriding priority now for the Baggies is a victory at home to Norwich on Saturday.
"It was a tough game against Manchester City who are a quality side and who have spent a lot of money to get the team they have," said Anichebe.
"We were resilient, we showed fighting spirit and we made a few changes because we've had a lot of games recently.
"We freshened it up a bit and we fought until the end and got two goals, which was good, but we definitely need to start picking up some points.
"Even though we fought well we conceded some goals that could have been avoided, but the game's gone and now we're looking forward towards Norwich. We'll bounce back on Saturday.
"We're not worried about our form because we've been playing so well, but sometimes things just happen.
"We just have to get back to where we were before, and we know what we need to do to do that.
"It's definitely going to happen. We'll keep fighting."