Arsene Wenger's side have made a slow start to the 2014-15 domestic campaign, with just four wins from their opening 12 league outings.
Last season's FA Cup winners came under heavy criticism for wasting a host of first-half chances in the 2-1 home defeat to Manchester United last weekend, but there was more positive news on Wednesday with a 2-0 victory over Borussia Dortmund.
That win secured their progress into the Champions League knockout stages with a game to spare, but Mertesacker knows the London club must now focus their attentions on addressing their league form, starting with Saturday's trip to The Hawthorns.
"We were very convincing [against Dortmund]," he said. "We have to show character and that is what makes me really happy for the next few games, because we have to sharpen up in the Premier League as well.
"Saturday is a good chance to show everyone that we are still alive. We have secured Champions League [last-16] football and that gives us a life, but that has nothing to do with the Premier League.
"We have to come back in the Premier League and that is the next target."
Arsenal have been hindered by a lengthy injury list this season, a problem highlighted by Jack Wilshere's latest setback, with the midfielder set for three months out after undergoing ankle surgery.
Mikel Arteta and Yaya Sanogo went off injured during the second half on Wednesday, with Wenger expecting the Spaniard to be out "for a while" with a calf problem, while the French striker - who scored his first goal for the club against Dortmund - has a hamstring problem.
Theo Walcott (groin), Danny Welbeck (knee) and Wojciech Szczesny (hip) all missed the midweek clash and remain fitness concerns.
Meanwhile, the hosts are looking to recover from back-to-back league defeats and they will be without midfielder Claudio Yacob after his red card in last Saturday's 2-0 defeat at Chelsea.
Defender Jonas Olsson is another certain absentee after it was revealed on Wednesday that he would be out until the new year, with the Sweden international set for an operation on his left foot.
Head coach Alan Irvine insisted on Thursday that Saido Berahino - who has seven Premier League goals this season - would continue to be selected despite being the subject of a police investigation into a possible case of drink-driving.
Defender Sebastian Pocognoli returns after hamstring trouble, although James Morrison is a doubt through illness.
Captain Chris Brunt is hoping Saturday can mark the start of a turnaround in their home form, with West Brom winning just once at The Hawthorns in the league this season.
"Points are hard to come from away from home in this league but in the last few months we've done a lot better away from home," he told The Birmingham Mail.
"I don't really know what that is. It's a difficult one to put your finger on but it's down to us to improve that.
"Arsenal will be favourites to win but we will be prepared for them. It's a big game against Arsenal followed very closely by another one against West Ham [on Tuesday].
"Our home form hasn't been great this season so we have two games that give us a chance to improve that."
