The Scottish midfielder saw his effort from 12 yards kept out by opposition keeper Mathew Ryan in the final stages of the contest at the bet365 Stadium.
Adam had to see off protests from Jese Rodriguez before stepping up to take the spot kick, with the 24-year-old - who won the pen -
visibly upset at being overlooked at a pivotal point in the match.
Speaking after the contest, however, Lambert claimed that it would be wrong to blame individuals, despite the missed attempt ensuring that Stoke remain in the bottom three.
"When you get a penalty in last minute it's a big opportunity to win the game. But the penalty's a lottery, a hit or a miss," he told Sky Sports News. "Nobody likes to see [players fighting over who takes a penalty]. Charlie scored the last one against Coventry and he felt confident he was going to score.
"I am a great believer that if you feel confident, step up and hit it. The lads are desperate to score and desperate to win and I think that is the big thing. But you do not want to see that probably in public, that is the thing I would go against.
"He did [want to take the penalty] and I will never curtail that in anybody if you have a great desire to score. I would rather have that than not and people shying away from it and that is one thing he never done. But the second half was very good."