The Gunners, with a makeshift defence and missing Mesut Ozil because of a knee injury, had taken an early lead through a fine finish from Alexis Sanchez and looked on their way to victory.
However, Hull quickly were on level terms through a controversial equaliser from Mohamed Diame as Arsenal claimed a foul in the build-up.
The Gunners were then made to pay for switching off right at the start of the second half when Abel Hernandez - only playing after an injury to Nikica Jelavic in the warm-up - headed Hull into the lead.
Arsenal, beaten at Chelsea before the international break, looked set for more frustrations before Welbeck slotted home in the first of six minutes of added time, and then almost snatched victory at the death through Kieran Gibbs, who was denied by stand-in Hull goalkeeper Eldin Jakupovic.
"We got a point but we had 80 per cent possession
It is a very disappointing result," said Wenger, who moved to allay any fears over an ankle/knee injury suffered by Jack Wilshere during the second half.
"We were unlucky with the referee on the first goal, but on the second goal we can only blame ourselves.
"We came out of the dressing room with a lack of focus and gave them the lead straight away
It was difficult.
"I cannot fault the effort or the heart that we had in the game
The defensive concentration was missing on the second goal and when you make it difficult at that level you cannot give the goals away like that."
Wenger added: "Even in the last five minutes we had three clear-cut chances on goal
It is difficult when we play against teams who are physically stronger and organised, it was 10 against 10 in one half.
"This was the kind of game where we couldn't afford to concede another goal when we came out at 1-1
We know that - we have enough experience to know that and we cannot give a goal away like we did.
"But we put our heart and effort in until the last second and I cannot fault the effort, the spirit and the work rate of the team."
Arsenal have now not won in the Barclays Premier League since September 20 and are some 11 points behind leaders Chelsea in sixth.
Wenger added: "Of course I cannot say it is not a concern, it is a big concern because the other teams win their games and we don't."
After looking set for being on the end of a hiding, Bruce was full of praise for his side's efforts.
"I am satisfied with a point, but I think that is four times this season we've conceded in the last minute," he said.
"Today I didn't think we were going to concede because we were comfortable, but we ran out of juice badly because the international players had been away and we made a few mistakes.
"I thought we were going to hang on to what would be a great win for us.
"However, I have been here before with teams where Arsenal have played the reserves and we have been beaten by six or five and gone away with our tails between our legs, so we have done extremely well to get a point."
Bruce revealed Jelavic had twisted his knee during the warm-up, while defender Michael Dawson also hobbled off in the second half with an ankle problem.
Goalkeeper Steve Harper, meanwhile, looks set for a spell out of action, having to be replaced just before half-time.
"It looks as if he has ruptured his bicep, which is a horrible injury," Bruce said.
"He would love me to say he did it when he tipped the ball over the bar from (Santi) Cazorla, but it was a shot somebody scuffed and he went down."
Source : PA