Pulis believes that his side played well enough to deserve to win the match, highlighting the performances of Jones and Jerome in particular.
"I thought we deserved to win the game - I would have been absolutely devastated if we hadn't won the game today," said Pulis.
"After the first half I thought we deserved to be coming in leading, but we just picked the pace up and the two subs made a great difference again.
"Cameron Jerome is a great impact player and he scored a great goal."
The win leaves Stoke 10th in the Premier League table.