Having blown leads in back-to-back Premier League games to put a top-four finish at risk, the Frenchman said it had been important to score early on the way to a comfortable victory.
Chilean winger Alexis Sanchez put Arsenal ahead after six minutes with a low drive from the edge of the area after a sharp turn, and doubled the lead with a free-kick before halftime.
The win took them to 63 points, two above Manchester City, and into the final automatic Champions League qualifying spot.
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"We're under permanent pressure for every single game, so it is important to have the lead early and focus on the way we want to play football," Wenger said.
"You want always to score early goals but in the Premier League... it is difficult for everybody. There are top, top teams who are behind us."
Wenger was relieved to the win after draws against West Ham United and Crystal Palace in the last two games saw Arsenal drop out of title contention and imperil a top-four finish.
"The regret we have is being in the lead against West Ham and being in the lead against Crystal Palace, and not to make the (three) points," he said.
EMPTY SEATS
There were a smattering of empty seats at The Emirates but Wenger said the unusual timing of the match might have played a role in that since there was still a lot to play for.
He noted that it was important to finish third rather than fourth, thus avoiding Champions League qualifiers in a calendar already filled with an expanded European Championship.
"Top four is not Champions League. Top three, yes, that is why it is important... When you have to play qualifiers, the European Championship is still going on," he said.
Even third spot won't be enough for his critics, especially with unheralded Leicester City and the Gunners' arch-rivals Tottenham Hotspur battling for the title.
Wenger said if Arsenal, who were once title favourites, kept winning then anything was possible and he rejected the idea Leicester's success had increased the pressure on him.
"We want to finish as high as possible. You never know what happens in front of you. There still can be twists and turns. But we want to win our games," he said.
"Because Leicester is in front, everybody thinks we should have done it (won the title). Yes, ok, but you can say that for any other team, because Leicester was at the bottom of the table last year, so you could say that all 19 teams could say that."
(Reporting by Alistair Smout; Editing by Ken Ferris)
