The FA Vase holders blitzed the Mariners with three goals in the first 11 minutes.
And while Shields fought back, reducing the score to 3-2, Bay kicked on again, leading 5-2 at the interval before completing a 6-3 victory.
Steadman believe
s his side came up against the Northern League champions elect, and said: "I have never seen a side play like that for 20 minutes.
"Manchester United couldn't have caused us more problems. They had us in our half for 20 minutes, and pressed and pressed. Everything they hit went in, from inside and outside the box.
"To be honest, I think we played the champions. We've played Spennymoor, Benfield and Bedlington recently, but Whitley Bay were superb."
Shields have hit a bit of a dodgy patch after their fine start to the season, but Steadman is refusing to get too concerned.
He didn't get carried away when his side were as high as fifth, and now that they have slipped back into the middle of the pack, he isn't getting too downbeat either.
He added: "I wasn't kidding myself one bit. We have lost a few games, but we're still mid-table.
"Results can give a false impression. As long as we give a good account of ourselves then I'm happy.
"I was happy with the performances against Spennymoor and Whitley Bay, but not with how we played against Benfield."
The tough run of fixtures continues for Shields tomorrow, when they travel to another side at the top of the table, Penrith.
The Cumbrians have been one of the surprise packages of the season, but lost 4-1 at home to Billingham Synthonia in midweek.
Steadman, who welcomes defender Richie Paxton back, added: "Penrith certainly aren't a Spennymoor or Whitley Bay, but they will be strong and always have a decent side.
"We don't fear going there. We will go there confident, but we just need to go on another run.
"I've seen enough in the squad to suggest we can – we just need to get rid of a few individual errors."
Dave Graham - September's player of the month – and Tony Coe, both sent off against Whitley Bay, will be available for the game.
