Bournemouth powered into a 3-0 lead thanks to goals from Charlie Daniels, Callum Wilson and Ryan Fraser, only to slip off the pace with captain Simon Francis sent off.
Alexis Sanchez, Lucas Perez and Olivier Giroud snatched a last-gasp draw for Arsenal, with Wenger again hitting out at the Premier League scheduling.
“We had three or four players we had to play tonight that we had to wait until the warm-up to see if they could play,” said Wenger.
“Hector Bellerin had a knock so he was uncertain to play, and that’s the problem with only 48 hours (between games); you have to play some players again.
“Laurent Koscielny too, and we had Gabriel (Paulista) that we didn’t start in the end.
“And then I didn’t start Alex Oxlade-Chamberlain because I didn’t take a gamble with him, because I didn’t know who we’d have to take off.
“This complicates the job a lot, but we have to shut up and cope with it.”
Bournemouth handed Arsenal a torrid opening hour, with Tottenham fan Daniels blasting a fine opener.
The ex-Spurs man’s crisp finish was backed up minutes later by Wilson’s penalty, with Granit Xhaka upending Fraser.
When Fraser bullied Bellerin and then slotted the ball between Petr Cech’s legs for Bournemouth’s third, the hosts thought they were home and hosed.
But Sanchez headed his 13th Premier League goal of the campaign, before Perez buried a stunning volley – and Giroud headed the equaliser two minutes into added time.
Giroud met his goal with a “scorpion kick” celebration, referencing his stunning flicked goal that sealed Arsenal’s 2-0 win over Crystal Palace on New Year’s Day.
Wenger admitted fearing Francis Coquelin could be set for a spell on the sidelines owing to a hamstring problem, while also batting away thoughts of a title chase.
The draw leaves Arsenal in fourth place, trailing leaders Chelsea by eight points.
“You don’t really speak about us and we don’t look around us at the moment,” said Wenger, of Arsenal’s title chances.
“Look I’m ready to play tomorrow again as long as we play against an opponent who has played today as well. That is what I call fair.
“For the rest, we have to play when we are told to play. But we want to play against teams in the same time of rest and preparation as we have.
“Coquelin has a hamstring (problem).
“It’s too early, we have to wait 48 hours for the scan and the result. But usually when he sits down and comes off it’s not so good news.
“If it’s just tiredness he will try to play on but he didn’t even try to play again.”