Speaking after the final in Porto, Pulisic told CBS Sports: "I can't explain it, it's still such a shock. I'm so proud."
He was watched by his parents and a number of friends from the stands at the Estadio do Dragao, making the occasion all the more special.
"I'm so thankful for all the support. To have people here today was amazing," Pulisic said.
"I knew I was going to have to put in the hard work defensively. I wish I put away the chance I had. I didn't quite get under it like I wanted, but in the end this team was always going to win this game and I'm so proud of them."
Plagued by injuries this season, Pulisic was able to bring father Mark and mother Kelley into the celebrations on the pitch to mark a happy ending to a tough campaign.
Pulisic added: "I have my parents here so I've just been speaking to them. I'm so proud to be here.
"It's been a difficult road for me and I couldn't imagine winning the Champions League ever in my life and now I'm here so it's just crazy."
While Chelsea's players head off to summer breaks or away on international duty, Pulisic said the aim next season would be to "come back and try to do the same thing".
Olivier Giroud, who played a significant part in Chelsea reaching the final, was an unused substitute against City.
But the veteran striker, who could have a big role to play for France at Euro 2020, was determined to enjoy the evening.
"It's extraordinary, we had a remarkable route, we knocked out some big teams like Real [Madrid], Atletico wasn't easy, Porto either, and tonight we played against a great team in City," Giroud told RMC Sports.
"It wasn't played out on a big thing, these kinds of matches are played out in details."
Giroud hailed the performance of player of the match and fellow Frenchman N'Golo Kante, whose action-packed display in midfield kept Chelsea moving forward.
"It's right that he was man of the match, he's huge, he won 50 balls, he hurt them," Giroud said.
"He's unbelievable, this guy. It feels like there are 12 players on the pitch with him. I'm happy for him.
"We're a bunch of friends and it shows on the pitch, I'm happy that our efforts have been rewarded. You could see our determination tonight and our desire to go out and get it."