Bowen, who is in England's squad for Friday's friendly against Australia and a European Championship qualifier against Italy next Tuesday at Wembley, earned all four of his England caps in the build-up to Qatar, making his omission from the squad all the more painful.
"I was disappointed to miss out but that's what happened," Bowen told reporters after training at St George's Park on Tuesday.
"I had to deal with it and all I could do is keep playing football to a level that I know that I can play at and everything will take care of itself.
"I had a really good pre-season, had some good games, scored goals there and you can take confidence and momentum from each game that you play.
"For me, that's all I've tried to be doing. Keep playing football with a smile on my face because you know that what makes me a good player... when I'm playing with a smile on my face."
His smile has been extra wide the past few days after getting the call-up from Southgate on Thursday and then securing a new seven-year deal with West Ham on Sunday.
Bowen has scored 45 goals in 167 games for the Hammers, including the winner in the Europa Conference League final against Fiorentina last June. He is West Ham's top scorer in the Premier League this season with five goals.
He could cap the heady week with his first appearance at Wembley.
"That would be the ultimate," Bowen said. "As a little boy you dream of playing for your country and you never think it is going to happen, but now I am here, I want to play at Wembley and hopefully I get the opportunity to do so."
Bowen said being a new dad - he and partner Dani Dyer welcomed twin girls in late-May - has made him more mature.
"You try and keep football away from home life as much as possible because you might have a bad game and you don't want to take it home to your children," he said. "It is just a special moment, every time you go home you are excited and when you finish a game you are excited to see them."
England top Group C with 13 points from five games, while Italy, Ukraine and North Macedonia have seven points apiece.
Southgate's side took a hit on Sunday when Arsenal manager Mikel Arteta announced Bukayo Saka (22) would not be available for October's international fixtures, due to a lingering hamstring injury.
