Unai Emery insists Arsenal will continue to take it "step by step" after a convincing 2-0 win over Southampton sent the Gunners fourth in the Premier League.
Alexandre Lacazette and Henrikh Mkhitaryan scored first-half goals at Emirates Stadium and the hosts had a succession of other chances to increase their tally.
With Manchester United held at home by leaders Liverpool and Chelsea playing in the EFL Cup final, Arsenal were able to gain a foothold in the race for fourth, but boss Emery is refusing to look too far ahead.
"We are thinking step by step, game by game and today we finished happy but we are preparing again for the game on Wednesday [against Bournemouth]," he said.
"Today, Chelsea are not playing [in the league], they are playing in the final and we are in the position at the moment and continue with the same idea."
Asked later at a post-match news conference if he regretted the fact Arsenal did not score more to boost their goal difference, Emery said: "We created chances.
"Today we can win with a bigger difference than the two goals. We need to continue to play with this intensity. Keep it for 90 minutes.
"Lacazette deserved to score more, Auba [Pierre-Emerick Aubameyang] had two moments when he was on the pitch. But my problem is when we don't create chances."
The impressive Alex Iwobi was withdrawn with around 15 minutes of the game remaining and appeared to be clutching his calf, but Emery assuaged fears over his fitness.
"I was just speaking with him, he said only it was only a knock," he added. "I hope he'll be okay for Wednesday."
Shortly before Lacazette's opener, Nathan Redmond wasted a gilt-edged chance to put Southampton ahead and Saints boss Ralph Hasenhuttl felt that miss shaped the game.
"I think the key moment was we had the chance for the 1-0 from Reddy and at other side received the first goal," he said.
"But, yeah, Arsenal in the first half were much better and played very simple, very good. We had problems to defend them."
Struggling Saints remain 18th in the table and a point away from safety ahead of a crucial home fixture with Fulham on Wednesday.
And Hasenhuttl acknowledged the importance of that clash.
"Of course, it's a very big game. We know the next weeks are tough at home against Fulham," he said.
"Yeah, we need to have a win, and I think we have to recover very well now for Wednesday's game and do everything to win this game."