Ex Celtic midfielder Lambert, a Champions League winner with Borussia Dortmund, admired how the Bhoys coped with the pressure of having to beat Spartak Moscow to reach the knockout stages.
The current Aston Villa boss said: "Celtic have done outstanding to get through. The group they had to get through was incredibly hard.
"To beat Barcelona in your own back yard was a fantastic achievement. The pressure on them the other night was monumental against Spartak and to deliver the result was fantastic.
"There is incredible pressure there that you have to live with every single day."
Lambert added: "Will there be more accent on Europe with no Rangers? I think so.
"You have to perform every single week, not just sporadically, because the pressure and history, what happened with the Lisbon Lions (in 1967).
"You are the first British team to win the European Cup and so you have the expectancy level and history level to perform at.
"If you don't perform, it can be unforgiving but they deserve the credit that has come their way.
"Maybe the league is not as strong as what it was but to do what they have done in Europe is a fabulous achievement."