Lambert's current side travel to Carrow Road to face the Canaries on Saturday as both teams look to move closer to Premier League safety with a victory.
"There's no sentiment in football. Would I prefer ourselves and Norwich to survive? No, it's all about us now," Lambert told reporters. "There are a lot of good people at Norwich, people I'll say hello to. I've got nothing but gratitude to that football club. We had a good time there together for three years.
"I have a lot of respect for Norwich City as a club and the fans were great to me over the three years.
"But my job is here now. When we won 4-1 there in the League Cup I didn't punch my fist in the air because I've too much respect for the fans at Norwich to do that."
Lambert succeeded in securing two successive promotions during his time with Norwich.