Lambert watched from the stands as United ran out 3-0 victor at Old Trafford in what proved to be a fairly comfortable win.
In his first press conference since being appointed manager at the bet365 Stadium, Lambert stressed that the worst defensive record in the league was not purely an issue for the back four.
"Paul has been successful in management at clubs with a strong and stable background and with local ownership the kind of foundation we are able to give to our managers", Stoke vice-chairman John Coates said.
"I'm honoured and privileged to be here and I can't wait to get started". It was the Potters' 13th loss in 23 league games and kept them 18th in the standings.
Lambert's appointment, apparently as third choice to succeed Mark Hughes, has been questioned in some quarters but the former Champions League victor boasts an impressive record of sparking an improvement at nearly all the clubs he has managed. The club shouldn't be in the position we are in. It is a long time being out and being thrown into the deep end so I know he is a real talent, Stephen Ireland, but you've just got to watch that you don't overburn him just because he's had such a long time out.
"This is not new to me".
"I'm looking forward to the relationship with the supporters and trying to get a winning team".
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"As a team we have to do better and stop conceding goals".
". We win as a team, we lose as a team".
He added: "I thought we showed really good signs for the new manager".
Stoke, now 18th in the Premier League, had been interested in Gary Rowett before he signed a new contract at Derby, and subsequently targeted Espanyol boss Quique Sanchez Flores and Republic of Ireland manager Martin O'Neill, both of whom removed themselves from the running.
"From day one, the fans are going to be vital".
His first match in charge will be at home to Huddersfield Town on Saturday.