Having opened the campaign with a slender win over Crystal Palace and then scrambled a draw at Everton, Arsenal was held 1-1 by a Leicester side playing in the top flight after a decade away.
Liverpool, though, recovered from its setback at Manchester City at the start of the week with a 3-0 win at White Hart Lane which ended Tottenham's perfect start to the season.
Aside from Arsenal, only three teams remain unbeaten. Chelsea and Swansea maintained their 100 percent starts on Saturday, while Aston Villa beat Hull 2-1 on Sunday to make it two wins out of three along with a draw.
Arsenal has shown in previous seasons it can recover from slow starts to still finish in the four Champions League places, but a push for the title is now expected by the London club's fans.
That could require a late addition to the striking options before the transfer window closes on Monday night until 2015.
''We are very active,'' Wenger said of Arsenal's transfer activity. ''We are disappointed not to get to get the three points. Let's not put that down to only missing a striker.''
But with Yaya Sanogo leading the strike force in place of Olivier Giroud, who is sidelined until at least late December, Arsenal lacked cutting edge up front.
When Sanogo fluffed a chance it was left to Chile forward Alexis Sanchez to score his first league goal in the 20th minute since joining from Barcelona in the offseason. But Leonardo Ulloa was able to equalize inside two minutes after meeting Jeff Schlupp's cross from close range.
''I think we lacked a bit of creativity and sharpness,'' Wenger said.
Everything Liverpool did have in abundance at White Hart Lane, having already strengthened its striking options following Luis Suarez's departure to Barcelona by signing Mario Balotelli last week. The Italy striker started on Sunday but lacked his cutting edge on his return to English football 20 months after leaving Manchester City for AC Milan.
''You could see his team ethic - he was pressing, working for us as much as he could. He was very good,'' Liverpool manager Brendan Rodgers said. ''Take away the circus that surrounds him - the circus he probably invites himself sometimes - and control the background noise and get him focused on his football, and he's a good fella.
''He'll make mistakes and he was disappointed not to score, but he'll be a handful for defenders.
But Raheem Sterling shone as the creative force after putting Liverpool in front in the eighth minute after neat buildup play by Jordan Henderson and Daniel Sturridge.
Liverpool took until four minutes into the second half to extend its lead courtesy of a softly-awarded penalty. After Joe Allen was held back by Eric Dier in the area, captain Steven Gerrard netted from the spot.
While there was no debut goal for Balotelli, defender Alberto Moreno did score on his second appearance for Liverpool. The left back dispossessed Andros Townsend on the half way line after charged down the left flank before dispatching the ball in the net on the hour.
The league now takes a two-week break for international fixtures.