The Gunners produced a much-improved, composed display to beat Champions League Group D leaders Borussia Dortmund 2-0 at the Emirates Stadium on Wednesday night, reaching the last 16 of Europe's elite with a match to spare
Mertesacker, though, believes the Germans' own domestic struggles in the Bundesliga - with Jurgen Klopp's side in the bottom three despite their fine European form - show focus must quickly turn towards getting things right at The Hawthorns.
Arsenal are eighth in the top flight after a 2-1 home defeat to Manchester United last time out.
Mertesacker said: "We were very convincing (against Dortmund)
Everyone had to learn.
"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 to everyone that we are still alive.
"Champions League football (in the knockout stages) we have secured and that gives us a life, but that has nothing to do with the Premier League
"Dortmund are a good example of that, because they are already through, but they have suffered a lot in the league
We have to come back in the Premier League and that is the next target."
Arsenal, who squandered a 3-0 lead against Anderlecht a fortnight ago to draw, will need results to go their way on matchday six to overhaul Dortmund and secure seeding for the knockout stage draw - with the likes of Bayern Munich, Real Madrid and Paris St Germain, just ahead of Barcelona in their group, potential opponents for runners-up.
Whatever transpires by the time Arsenal's next European fixtures come around in February, manager Arsene Wenger will be hoping to see some key men back from injury.
Midfielder Jack Wilshere is expected to face several weeks out after damaging ankle ligaments against United, while captain Mikel Arteta is also being assessed after limping off on Wednesday night with a calf problem.
Goalkeeper Wojciech Szczesny was sidelined by a hip problem, but should return at The Hawthorns, with striker Danny Welbeck rested because of a minor knee injury as was Theo Walcott (groin).
France forward Olivier Giroud - who scored on his return from a broken leg against United - was ineligible after not being included in Arsenal's original European squad, so will be pressing for a start this weekend, while defender Laurent Koscielny was on the bench against Dortmund after recovering from an Achilles problem.
Yaya Sanogo was substituted late on after pulling up with a tight hamstring, having earlier fired home his first senior Arsenal goal inside just two minutes.
Midfielder Alex Oxlade-Chamberlain, who cracked a superb 25-yard volley against the crossbar before Alexis Sanchez swept in a well-taken second goal on 57 minutes, is confident Arsenal can now build some momentum.
"Wins always relieve pressure, When we win everyone's happy
The players, the manager, the staff and the fans are happy," he said.
"There is a long way to go in this competition and the league
We need to try to back this win up with some good results in the future."
Source : PA
Source: PA