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Aaron Ramsey's 12th-minute goal gave the Gunners their eighth straight Barclays Premier League victory which leaves them four points behind leaders Chelsea, although Jose Mourinho's men have two games in hand.
Wenger said: "Nothing has changed - we need a perfect run and we need a non-perfect run from them but we can't master that, we can only master our own position.
"We want to keep winning because we have to look behind us as well at Manchester United and Manchester City.
"We are consistent and we have a good attitude in the team so it is a challenge for the team and we have to focus and win the next game."
Wenger was particularly pleased with the way his side coped with Burnley's physical threat and paid a rich tribute to the performance of Sean Dyche's men, who came close to salvaging a point through late chances for George Boyd and Danny Ings.
The Frenchman added: "I was surprised by the quality of Burnley and it will be a shame if they go down because they have done fantastically well.
"They are organised, they press well and they show great solidarity. They are very fit and I understand now why they took points from the big teams.
"You have to fight and be combative until the end and we couldn't score the second goal but the defence played very well today and got us the three points."
