Swansea dominated early on and led through Andy King but goals from Badou Ndiaye and Peter Crouch gave Lambert his first away win since taking over in January, and he praised his players' response to their poor start.
“It was tough at times, for the first 20 minutes I thought we were awful, we looked anxious and lethargic but we somehow came back and took the lead," Lambert said, quoted by Stoke's official website.
“At the break I said a few things that I felt needed to be said and we looked a better side out there. We had to defend bravely and make some big challenges and saves, but we made them and we came through the game.”
Lambert also spoke glowingly of Stoke's supporters. Almost 2000 of them travelled to South Wales and made most of the noise, including a rousing rendition of Delilah at full time.
“The supporters were absolutely incredible out there again today, and I honestly can’t give them enough credit," said Lambert.
“It has been a tough year for everyone connected to this fantastic club, especially the supporters, so for them to give the lads that backing today was unbelievable.
“I feel for them, I really do because they turn up week in, week out in such large numbers and they have been let down massively this season.
“It’s not a nice feeling at the moment, it is tough and it is all still very raw, but we won the game today and before the start of play that is what I asked of the guys."
It remains to be seen whether Lambert will remain at the Bet365 Stadium next season, as his contract contains a clause allowing the club to terminate his contract at the end of June if they so choose.