Strikes from Mohamed Diame and Abel Hernandez looked set to condemn Arsenal to a second successive Premier League defeat on Saturday.
However, Alexis Sanchez - who had opened the scoring after 13 minutes - jinked through Hull's defence in injury-time to set up Welbeck's equaliser.
The draw salvaged a small positive for Wenger, who saw Jack Wilshere hobble off in the second half, but the Frenchman was unhappy with Arsenal's defending for Hernandez's goal shortly after the break and referee Roger East's refusal to award a free-kick for a perceived foul on Mathieu Flamini during the build-up to Diame's opener.
"It was a disappointing afternoon because I think we had 80 per cent possession and got one point," Wenger said.
"It is a very disappointing result. We had absolutely to win this game. We were unlucky with the referee on the first goal but on the second we can only blame ourselves.
"We came out of the dressing room with a lack of focus and gave them the lead straight away. I cannot fault the effort, the heart, but the defensive concentration was missing for the second goal.
"At this level you can not give goals away like that."
Following Hernandez's goal, Hull were pegged back for large stages of the second half until Welbeck eventually found the net.
The result leaves Arsenal 11 points behind leaders Chelsea and Wenger admits the gap to Jose Mourinho's men is a concern.
"Of course I can't say it's not. It's a big concern," he added.
"It was 10 against 10 in one half and it was difficult. This was another game where you cannot afford to concede another goal when you come out at 1-1.
"We know that. We have enough experience to know that and we cannot give goals away like we did.
"I think the first goal is for the referee, honestly. The second goal is for us."
