Despite Monday's win over Newcastle opening up a four-point gap between themselves and fifth place, the Frenchman insists Champions League qualification is not secured yet.
Since losing to Everton at the start of April, Arsenal has reached the final of the FA Cup and won all three Premier League games to build a four-point cushion between themselves and the fifth-place Toffees.
However, Wenger warned that their place in the Champions League for the 17th consecutive season is not guaranteed and urged his charges to continue their fine form against West Brom on Sunday.
"[The Newcastle win] is a step forward but we need to make another one because we have another home game [on Sunday]," he said. "It is another opportunity to win again. What is important is to focus on our performance. Game-by-game, they look strong and convincing now.
"We have to live with reality. We have shown quality but at the moment we have 73 points, we can make 79. Let's finish as high as we can and analyse after where we can improve, what was right and what was wrong."
Wenger also highlighted this month's FA Cup semifinal win against Wigan on penalties as a turning point, after Arsenal required an equalizer eight minutes from the end of normal time to avoid an upset.
That has left the London club on the brink of a first piece of silverware since 2005, with Hull City awaiting it in next month's final.
"Wigan was a big game of pressure because the last thing you want is to be 1-0 down with 10 minutes to go of an FA Cup semi-final against a Championship team," he said. "It was certainly important on the confidence front."