Irony or bitterness, as of tone
"Exactly," she said with enough sarcasm that he chuckled.
She took his sarcasm as a sign that he felt better.
Kara took the joke seriously because she was too credulous to understand the sarcasm.
It was hard to tell whether the sarcasm had gone over his head or he simply wasn't amused.
His words were spoken with sarcasm, but not for the reason Alex probably thought.