Lambert said: "I'm devastated for the players.
"When you get a penalty in the last minute it's a big opportunity to win the game. I think the second half we were well on top, we got a great goal. Brighton I thought had done really well in the first half, made it difficult. We changed the system in the second half.
Stoke had come back from a goal down with a Shaqiri strike and missed a stoppage time penalty that would have given them a crucial three points in the battler to avoid relegation.
"Brighton had obviously scored a great goal themselves so credit to them for that. The second half, when we made a change, we were much better. We scored and had some great opportunities and the penalty... yeah, the penalty's a lottery.
"It's a hit or a miss really. Charlie scored a few weeks ago, at Coventry I think, before we came in so as he felt confident so the confident person hit it."