Shawcross miraculously cleared a goal-bound effort off the line in stoppage time, to deny his Bosnian international teammate would have been a cruel winner.
"It was a great clearance from Ryan right at the end to be fair to him," Begovic told Stoke's website. "As soon as the ball went over me I just thought to myself 'oh god it's in', and prayed for somebody to get back and hook it clear."
Begovic added: "It was a dry pitch out there, so Ryan did remarkably well to get back and clear it away in the manner that he did. He was great again today, but so was every other player who featured today.
"Like I say, we deserved that result, and we can go to Chelsea in a week's time knowing that we are capable of mixing it against that sort of team."