Mauricio Pochettino's men lost 2-0 against the Bundesliga outfit, thanks to second-half goals from Klaas-Jan Huntelaar and Joel Matip.
However, Lambert, the club's top scorer last season, is not reading too much into the result.
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"They are a few weeks ahead of us in their pre-season so we're not too worried about losing two-nil," he told the club's official website.
"If we won six-nil, we wouldn't be thinking we were the best team in the world.
"It's about getting your fitness in – I and some of the lads played for 70 minutes, and that will help me come the [start of the] season."
As well as gaining fitness, Lambert also feels the pre-season tours of Spain and Austria have enabled the club's new recruits to bond.
Pochettino has brought in midfielder Victor Wanyama and defender Dejan Lovren, with both settling in well according to Lambert.
"We've been together, and we've got to know the new lads and welcomed them in. We're getting closer as the days go by," the 31-year-old continued.
"It was nice in Spain, where they had a little secluded spot for us that really helped the boys bond, and now we've come to one of the best hotels I've seen in my life."
The club will continue their pre-season build up against Besiktas on Saturday before taking on Spanish sides Celta Vigo and Real Sociedad.