Lambert - whose third child was born on the same day he was called up for the Scotland game - said he was "overjoyed" with how the last few days had gone for him.
He told Southampton's official website after the Albion match: "It's a great way to finish the week.
"It'll be a week that I'll never forget in my life and to finish it off with a win for Saints is superb."
On his penalty, he added: "I tried to just whack it into that corner and thankfully, it's gone right into the corner because I think he (Baggies goalkeeper Ben Foster) has got fingertips to it as well.
"I knew I'd caught it sweet because it would have been a hell of a save, if he'd saved it."
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