Bruce says he is the current "whipping boy" among Premier League managers, with the Black Cats yet to win this season and having been on the end of a damaging home defeat by Newcastle already.
But he insists club owner Ellis Short and chairman Niall Quinn know he needs more time to let the new-look squad settle down.
Bruce said: "I was away with Niall and Ellis only two days ago and I know the relationship I have got with them I can't for granted.
"Ultimately we are in a sports industry which needs results. They are disappointed with the results, of course they are.
"They also understand that with the job I have done over the last couple of years surely I need a little bit more time than just three or four games in.
"Thankfully I am convinced they think that way too. We need to hit the ground running and get a couple of wins and that's normal in the Premier League."
Bruce is confident that Sunderland will still finish above their north-east rivals Newcastle, but he knows that for some fans a home defeat by the Magpies mattered more.
"We had a bad result against Newcastle and it has created this frenzy," he said.
"I still believe we will finish above Newcastle, that's the aim, but in certain people's eyes that's not enough, the one-off game is all that matters. That's the way it is up here unfortunately.
"The lads who have come here now know what the north-east is. They are scratching their heads saying 'Dear oh dear, that's a bit brutal', but I have just reminded them about the intensity of playing here."
John O'Shea could return to bolster Sunderland's defence at home to Stoke on Sunday.
The Republic of Ireland defender missed the defeat by Chelsea due to a calf strain but has returned to training. Young striker Connor Wickham could make his first start since the 18-year-old's move from Ipswich.
Bruce admits Sunderland can ill-afford to slip up against a Stoke side who have made a strong start to the season.
He added: "We need to get a result. At the moment I'm the whipping boy, a few weeks ago it was Arsene Wenger.
"There will be a lot of managers saying, 'Thank God it's him, it's taking the heat off myself'."