City led twice in north London through Leroy Sane - who gave his team the lead after just five minutes - and Sergio Aguero, with Theo Walcott and Shkodran Mustafi netting in the first and second half respectively to get the hosts back on level terms.
Chances were in short supply after the German's 53rd-minute header, though, the result leaving City 11 points back from league leaders Chelsea, while Arsenal are seven points outside the Champions League qualification places.
And Welbeck praised his side for responding to going behind but was left frustrated by their failure to force a winner, with the pressure on manager Arsene Wenger, who is out of contract at the end of the season and facing calls to quit, unlikely to have eased.
"I think we have to look at the performance and see where we conceded the goals," Welbeck told Sky Sports. "Great character from us to respond in the way that we did.
"Obviously at this point in the season, it's not good enough for us. We want to be further up the league. We dropped two points. It's something we're going to have to build on in the next game," he added, referring to Wednesday's home match against West Ham.
"Two attacking teams, two teams who want to play with the ball, have possession. A bit of a cagey game in these sort of surrounds. [But] we wanted the three points."