The Gunners, who had two scoreless draws to kick-off the campaign, beat the Reds 2-0 at Anfield to make it three clean sheets on the trot, allowing them to move to eighth on the Premier League table.
German centre-back Mertesacker suggests it was a confidence-boosting victory and is excited about upcoming fixtures following this week's international break.
"We had to believe a lot, because our squad has had many changes and some important players have moved. We didn't know where we stood, but we are very happy now.
"We now have to focus on our strengths and that is vital for the next few weeks, to stay near the top of the league.
"A lot of challenges are coming after the international break but we are looking forward to them because we are full of confidence. We showed that against Liverpool."