The Nigeria frontman made his Albion bow in Saturday's 1-1 Premier League draw at Fulham following his £6million switch from Everton during the transfer window.
During his spell at Goodison Park, Anichebe received some criticism for a lack of goals but the 25-year-old is determined to set that record straight, as well as improving his all-round game.
Anichebe, who scored just 18 goals in 131 Everton appearances, insists he is determined to impress Baggies boss Clarke but would rather remain out of the spotlight in doing so.
"The sky is my limit but I'm not a selfish player and I don't need the headlines," Anichebe told the Birmingham Mail.
"Hopefully I can keep improving. I'm a team player and I have no problem holding the ball up for the team.
"I'm maturing all the time and in addition to holding the ball up well, I want to get on the end of chances.
"I'll take a battering if that's what the team need me to do. That's what I do and I think most people who've seen me play know that."
Anichebe was unable to get off the mark during his West Brom debut at the weekend but was found in strong positions, something he hopes to replicate throughout the season.
"Hopefully I can keep doing what I did on Saturday but I want to get some goals as well," he added.
"I have to mix it up sometimes. If I can keep adding different qualities to my game, I will improve. I have a lot of other qualities to my game as well but when the team need me to I will offer my strength.
"Steve [Clarke] is already telling me to do some different things. He wants me to run in behind defenders. That way people may not be able to predict what I'm going to do. I'm still young and I have plenty of time to improve."
The Nigeria international did come close to opening his Albion account, only to see his effort repelled by David Stockdale after he rounded Brede Hangeland.
"I thought I should have scored," he said. "I was on the spin, it was my first game and hopefully next time I'll score it.''