The 22-year-old was the Blues' joint-top scorer in the Premier League last term, but that was not enough to convince Roy Hodgson to take him to Poland and Ukraine.
Sturridge told The Jamaica Observer: "I feel hurt, but you know, maybe it is a blessing in disguise.
"It's going to spur me on to do better. It's going to drive me to want more success and to be a better footballer. I'm upset about it, but not too much."
Micah Richards had also been backed for a place in Hodgson's squad, but saw Liverpool youngster Martin Kelly called up as a late replacement for the injured Gary Cahill instead.
The Manchester City man also admitted he was upset at not being involved but vowed to come back stronger next campaign.
He said: "It's a real disappointment for me, you know, but it won't stop me from wanting to do more or do better next season."
Both players' clubs have enjoyed huge success this season. Sturridge was involved in Chelsea's incredible run to the Champions League final and claimed that being part of the club's European triumph was the "highlight" of his career to date.
"Winning the UEFA Champions league is the greatest achievement for any club," he explained. "And I am just happy I was a part of a Chelsea team that created history in doing that.
"Having that medal is the highlight of my career."
Richards also won silverware this year with City winning the Premier League thanks to a stunning last-day victory over QPR and described his delight at coming out on top of local rivals, Manchester United.
He added: "It was the first time in 44 years that City's won the Premier League, so for me to have that medal and lift that trophy was just amazing.
"I've been at City since I was 14 and to see us come first against the likes of Manchester United and Chelsea is just a massive achievement."
The entire campaign hasn't been all positive for the defender who admitted he had been involved ina training ground bus- up with one of City's more colourful stars.
"It was with my teammate Mario Balotelli," Richards revealed. "We were in training and we were losing a five-a-side game and he wasn't running like I wanted him to.
"I told him to run and he told me to shut up and, well, that really upset me. But Mario is my good friend, so it worked out fine."