Lambert proud of Norwich players after victory over Sunderland
Centre-back Leon Barnett put the Canaries, who had won at Bolton last week, in front in the 31st minute after winger Elliott Bennett had skipped into the right side of the penalty area, and Wales forward Steve Morison made it two after the break.
Lambert told Sky Sports 1: "It's not easy standing there when the lads have given you everything they have and with James coming off we were down to 10 men for the last little bit but I'm delighted we saw it through.
"It's a start. Winning away last week at Bolton was terrific and getting your first win at home is a big step. We're new to it but we're playing very well at the minute.
"I'm delighted for the lads. People maybe wrote them off a little bit with where we've come from. A few years ago we were in League One and now we're competing at this level and I think it's testament to the players."