The Canaries secured back-to-back victories with a win over Steve Bruce's men to go ninth in the table ahead of the weekend clash with Manchester United at Old Trafford
Goals from Leon Barnett and Steve Morison were enough to secure all three points over Steve Bruce’s side – who grabbed a late consolation from Kieran Richardson – to grab back-to-back victories following last weekend’s triumph over Bolton at the Reebok Stadium.
"It’s a start [with regards to the club's hopes of staying up]. Winning away last week at Bolton was terrific and being at home and getting your first win at home is a big step for us," Lambert told Sky Sports. "We’re new to it [the Premier League] but we’re playing very well at the minute.
"We’ll do everything we can to try and stay in the league, that’s first and foremost. Everybody will tell you the same.
"I think Brendan [Rodgers] will tell you at Swansea and Neil [Warnock] will tell you the same at QPR. We’re trying to get our foothold in the league, it’s a very difficult league, but as I’ve said before we’ve earned the right to be in it."
Next up for the Canaries is the daunting trip to league leaders and reigning champions Manchester United, and while Lambert concedes it will be tough test for his side, he’s delighted for his players to get an opportunity to mix it with the country’s elite.
"An easy game that one, the bus and everything will be going up to that one," joked Lambert.
"We’ll do everything we can. It’s a blip that [United's draw at Stoke]. They’re a top, top side and any team going there is going to find it really tough but we’re going to go there and try and do well.
"I hear people say ‘go and enjoy it’ but it’s only enjoyable if you’re holding your own. Manchester United, in my view, are probably the best team in Britain at the minute."
"I’m delighted for the lads [being in the Premier League] and the fans," Lambert added.
"They’ve been through some barren times and I think the numbers that they come, the away support is terrific.
"The lads I’m delighted for. People wrote them off a little bit and where they’ve come from two years ago when we were in League One and now we’re competing at this level and I think it’s a testament to players."