A 39th minute goal from Sadiq Ibrahim was enough to separate the two-time World champions from their South American opponents.
"I'm a bit disappointed in the play because that's not how we play," Fabin said.
"We kept the ball and passed it around but it looked as if we abandoned our style and we were trying to play long balls like the Colombians but it was not working for us.
"However, I'm a bit happy because it's group stage and to have taken three points in your first match, it's good, it's very good, so I'm happy for that. I'll also give credit to our goalkeeper and the defence, I think they did tremendously well," he said.
He added: "We had more chances than they had especially in the first half and getting into the second half. We could have buried them under goals so we deserved the win."
United States defeated India 3-0 in the other group game to top the log and they will lock horns with the Black Starlets in the next game at the Jawaharlal Nehru Stadium on Monday. A win for each of the countries will secure their qualification to the next round of the competition with a game to spare.