Begovic gifted Papiss Cisse an opening goal before Stoke's storming comeback.
He said: "It was personally very disappointing. I would have liked to do a little bit better with that but thankfully the guys bailed me out in the end. We've been playing really well at home so it would have been a shame to lose our run to that.
"I think it was a big three points for us. The guys that came on really changed the game, gave us some extra energy. After going a goal down we really pulled it back.
"I think it's a great three points, it really kicks us on and we can be happy with the result."