A 1-0 success at Turf Moor on Saturday continued Arsenal's fine run of form and, despite Wenger's public claims, means the north London club are involved in the title race.
Arsenal also remain in the hunt for the FA Cup, with a semi-final against Reading at Wembley next up on Saturday.
"We don't want to stop the run," said the Frenchman.
"There's a good attitude in the team and a great quality. We've won 16 of the last 18 so we are consistent.
"Let's see. It's a challenge for a team not to forget how much it hurts to lose a game and focus on winning the next one.
"We want to keep winning of course, because we have to look behind us as well. Man City, Man United, and after that you have three with Southampton, Liverpool and Tottenham as well.
"But we have made a little distance with them now. But Man United and Man City are behind us as well.
"We are in the FA Cup semi-final, we have six games to go with 66 points and we want to continue our run now."
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