Arsenal took a big step to securing their place in the Champions League for a 17th consecutive season after a comfortable 3-0 home win against an increasingly woeful Newcastle United on Monday.
With two Premier League games remaining, Arsenal have 73 points, four clear of fifth-placed Everton who lost 2-0 at Southampton on Saturday and have still to play title favourites Manchester City.
“One more win and we will be in the top four for sure,” Wenger told reporters, while injecting a note of caution. “I'm long enough in the job to know to get over the line is always difficult.”
Arsenal, who will face a European side in a playoff to reach the Champions League proper if they finish fourth, opened the scoring in the 26th minute through Laurent Koscielny when he prodded home Santi Cazorla's free-kick.
Mesut Ozil then doubled the hosts' lead in the 42nd minute with a tap-in after Tim Krul had twice denied Olivier Giroud.
Arsenal were rarely threatened and added a third after 66 minutes with a powerful Giroud header.
Arsenal's 3-0 humbling at Everton earlier this month looked to have ended their hopes of Champions League qualification but a run of three successive victories coupled with Everton's stuttering form has the Gunners back in the driving seat.
“We have gone through a difficult period and Goodison Park was one of them,” said Wenger.
“The spirit in the team is strong, determined and healthy and you can see that in the way we have bounced back from disappointment.
The Gunners dominated possession early on but failed to create any clear chances.
When the first goal did come it was through the unlikely source of centre back Koscielny, who got the faintest touch on Cazorla's teasing delivery.
Arsenal could have doubled their advantage immediately but the in-form Lukas Podolski was thwarted by Krul twice within two minutes.
Ozil did what his German international team mate could not and added a second with a simple finish after Krul had pulled off an impressive double save at the feet of Giroud.
Ozil then turned provider with a wicked cross for Giroud to power in his 15th Premier League goal of the season.