Lambert only played in the Premier League for the first time last season after a career spent in the lower leagues. But he scored 15 goals and ended as the joint leading English goalscorer, with Chelsea midfielder Frank Lampard, in the top flight.
"I've dreamt for it to go like that for a long time and for it to have gone like that was a dream come true," he said.
"It's probably the best header I've headed in my life."
"I saved it for the right time. It was a terrific ball by Leighton Baines, I managed to lose my marker and he put it exactly where I wanted it.
"I've tried to enjoy it, but my focus was to try and do well."
Only the group winners are guaranteed to make it to Brazil, with the eight runners-up with the best record against the teams finishing first, third, fourth and fifth in their section going into the play-offs.
Ahead of the vital competitive fixtures, manager Hodgson was glad his side did not have a "stroll in the park" on Wednesday.
England 3-2 Scotland: Rickie Lambert reflects on dream debut
"We have done very well to win the game," the 66-year-old said. "We came from behind twice, going behind against the run of play twice.
"We had to pull out all the stops to get back. I thought we dominated the game. It was a victory which was very hard fought.
"We didn't want a stroll in the park before the games in the autumn. We want to know we can come from behind and create enough chances."
Scotland took the lead when James Morrison's long-range effort was fumbled into his own goal by Joe Hart but Theo Walcott equalised after being put through by an excellent Tom Cleverley pass, while Danny Welbeck rose to head in a free-kick shortly after Kenny Miller's sharp turn and finish had given the visitors an early second-half lead.
And within three minutes of coming on, Lambert headed England in front from a Baines corner.
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