Norwich's first top-flight away win in 17 years was confirmed despite 10-man Bolton Wanderers hitting back through a Martin Petrov penalty - and John Ruddy pulling off a stunning save to deny David Ngog at the death.
Lambert said: "We have discovered the Premier League is unforgiving but the performance levels have been excellent and if they continue at both ends of the pitch we will be okay.
"I've seen Swansea City and QPR play and it shows the three teams that came up are very good. I think they are more than capable of holding their own but all we can do is concentrate on ourselves.
"We have got Sunderland at home coming up and then an easy trip to Old Trafford. But we have earned the right to play in this league and we make no apologies for going out and trying to win games."