Andreas Weimann had put Villa 2-0 up just after the break, but Javier Hernandez then claimed a hat-trick to deny Lambert's men.
But the Villa boss had nothing but praise for his young side after the game.
"We gave it absolutely everything, we were brilliant, the effort was great - but we are standing here and they do that week in, week out and they did it last year when I was at Norwich," Lambert told Sky Sports.
"They don't just do it to us, they have done it to loads of teams over the years and that is why they are where they are, it is not rocket science - you can't fault the team, we have a lot of young lads and they will take a lot of belief out of it but they can't give me any more. The effort, they were brilliant.
"We are a good side, we really are, we have a lot of injuries but the atmosphere was incredible but I can't ask any more from my players.
"They will keep going again, but they have been playing well."
Lambert could not single out any one player, finding positives throughout his team.
He added: "They are young players coming through, I thought Benteke was absolutely outstanding, and Agbonlahor is playing outstanding at the moment so it is hard to single out as they are playing so well."