Stoke had reason to be thankful for the gusts swirling around the Britannia Stadium when Begovic found the net in bizarre fashion after just 13 seconds - courtesy of a clearance that bounced over the head of opposite number Artur Boruc.
Despite the freak goal, the hosts were unable to end their winless run in the Premier League, which now stretches to seven games, as Southampton fought back impressively to claim a 1-1 draw.
Hughes was content with a point, but bemoaned the impact of the weather.
"Unfortunately the conditions spoiled the game somewhat," the Stoke manager said.
"It was a fortunate goal, quite bizarre really, and we're grateful for it, but with hindsight the wind was more difficult to play with than against. The wind wasn't great for both sides in the end."
Stoke opted to play with the gales behind them in the first half, but could hardly have anticipated what was to follow from Begovic.
Hughes added: "We wanted to take advantage of the conditions and we did. Obviously we weren't expecting our goalkeeper to do it for us, but give him credit - it was a great strike.
"He got his foot through it. Technically he was perfect. He's very pleased with it, obviously, and he tells me he's looking to score a few more.
"You could tell - as soon as the two centre-halves made the decision to let it bounce - that the goalkeeper (Boruc) was going to be in trouble. He was never going to get anywhere near it."
Stoke, who have not won in the league since August, are just one point above the relegation zone, but Hughes remains upbeat.
"It's a good point given the circumstances of the game, the conditions and the opposition we were up against," he reasoned.
"I think everybody saw once again that Southampton are a very good team. They've gone to places like Old Trafford and Anfield and got positive results, and they've got another one here.
"We were fortunate with the first goal, but we had good chances in that first half.
"At 1-0 you know there's always a chance they might get an opportunity and take it. I think both teams in the end will be comfortable (with a draw)."
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