Remarking on his sensational victory, the British driver also said he recited a "long, long prayer" before the contest in Hockenheimring on Sunday.
Asked during a FIA post-race press conference whether he ever thought he could have won, the 33-year-old answered: "I did.
"I mean, it's obviously very, very difficult from that position and highly unlikely, but you've always got to believe.
"I said a long, long prayer before the race started.
"We did the parade lap, I could see how much support I had out there and I just wanted to stay collected, stay calm."
The Mercedes driver has regained the lead position in the F1 2018 standings, with a 17-point advantage over second-placed Sebastian Vettel.
I wish I could describe this feeling right now... What a day, true proof that you should never give up!! The team did such a great job as they always do, I can't thank them enough! I kept the belief and it came true. A big, big thanks to God #Godisthegreatest @MercedesAMGF1 pic.twitter.com/5j3VBNFpJA
— Lewis Hamilton (@LewisHamilton) July 22, 2018
The German, who competes for Scuderia Ferrari, had been leading in the race before sliding off the tarmac during the 52nd lap, amid wet conditions.
Hamilton, who has spoken out about his faith before, continued: "But the team did such a great job, the car was fantastic today.
"Honestly, I'm so grateful.
"I would never have though you could do something like that today, but I just kept pushing, I kept believing and it happened.
"I really manifested my dream today. So big, big thanks to God."
Hamilton also received a reprimand from stewards after changing his mind about a pit stop.
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