Begovic netted with a wind-assisted punt that bounced over Southampton counterpart Artur Boruc 13 seconds into a tie at the Britannia Stadium on Saturday, which ended 1-1.
Begovic joined Peter Schmeichel, Paul Robinson, Brad Friedel and Tim Howard in the elite club of scoring shot-stoppers.
"I definitely meant it," Begovic joked in The Independent.
"It was nice. I've never scored a goal so I'll take it. I've never come close as I've never been allowed up for corners but it happened to go in.
"I didn't think it was going in at all and when it went in I thought 'What?'.
"It was a little bit surreal but the ball got caught in the wind and carried a distance.
"I'm in pretty good company so I'll take it as it helped us get a point.
"It was a shame we couldn't carry it on and get a second goal and really get on the front foot.
"But Southampton have been on a great run and are full of confidence so we knew it would be tough.
"We had to graft out a result but we'll take the point and take the positives out the game."