"The guys know they can step it up and they will step it up," U.S. coach Jurgen Klinsmann said.
While the Americans didn't play nearly as well as they're capable of, Klinsmann insisted his team did not take the opposition lightly.
"There's not the expectation just to kind of overrun Antigua or whatever country maybe that looks kind of weak on a piece of paper. They came here. They played the game not of their life, but for them it's big time. They gave everything they had," Klinsmann said. "It's important the players understand what they did OK and what was not so OK. They're going to hear that from me."
Bocanegra put the Americans ahead in the eighth minute, tapping the ball into the net after goalkeeper Molvin James made a diving stop but spilled Gomez's header off Landon Donovan's corner kick. With his 13th international goal, Bocanegra tied Marcelo Balboa's record for American defenders.
Dempsey's 26th international goal came on a penalty kick in the 44th minute after Marvin McCoy upended Donovan streaking into the area.
Peter Byers scored in the 65th minute for Antigua, a nation of about 88,000 that almost could fit its entire population in 65,000-seat Raymond James Stadium. Gomez restored a two-goal lead in the 72th after his initial shot and Michael Bradley's followup both were blocked.
Antigua coach Tom Curtis said his team proved it belongs.
"It's a testament to how far (we've come) that we're probably feeling a little disappointed with the result," Curtis said "I said to the players afterward, they should feel proud of themselves in terms of performance, but to be honest, we're a little bit disappointed that we didn't get even closer. If you had told me that two years ago that little Antigua would get that close to the United States and the players still be disappointed, I would have told you you were mad. We could have done things a little better, but we got close and gave them a fright."
It was a costly night for the No. 28 Americans, trying to qualify for their seventh straight World Cup. Third-choice left back Jose Torres was stretchered off after injuring his left ankle during a tackle in the 54th.
Torre's injury initially was described as an ankle bruise. Klinsmann said the player will have X-rays and be evaluated over the weekend.
"It's not looking very good right now," Klinsmann said.
After Torres came out, Bocanegra shifted to the left, and Oguchi Onyewu entered only to overcommit and allow Byers to come in alone on goalkeeper Tim Howard.
"I think Antigua did a very good job defending. They made it very tight. They made it difficult for us to create more chances," Klinsmann said.
Usually a possession-oriented midfielder, Torres started at left back following injuries to Fabian Johnson and Edgar Castillo. Klinsmann left himself potentially short at the position by omitting Eric Lichaj from his 23-man training camp roster. If Johnson can't return from his calf injury for Tuesday's qualifier at Guatemala, Bocanegra appears likely to start at left back.
"Those games are tricky," said Klinmann, a former German national team star and coach. "At the end of the day, I think the three points is the starting point that we wanted to have. We have that. We know obviously after a evening like that that we have to step it up a lot going into Guatemala, which we will do."
Two teams from the group, which also includes Jamaica, advance to next year's six-nation regional finals, which will produce three qualifiers for the 2014 tournament in Brazil.
After going 6-5-2 in exhibitions after Klinsmann replaced Bob Bradley as coach last July, the Americans played their first competitive match since blowing a two-goal lead and losing to Mexico 4-2 in the final of the CONCACAF Gold Cup last June 25.
Terrence Boyd, the 21-year-old son of an American serviceman and a German mother, entered in the 79th minute on a rainy night and now is tied to the United States in international competition.
Klinsmann started an offense-minded 4-3-3 formation, with Maurice Edu, Jermaine Jones and Bradley in the midfield, and Donovan, Dempsey and Gomez up front.
The U.S. failed to dominate possession in the lategoing and seemed to have heavy legs. Still the Americans outshot Antigua 19-7 and had a 14-2 advantage in corner kicks, including 9-0 in the first half.
While Antigua had few chances in the first half, Dexter Blackstock was in position to test Howard in the 38th minute only to have his shot blocked by center back Clarence Goodson. Antigua's players grabbed the sides of his head in disbelief.
"We can play better," said Bocanegra, the U.S. captain. "It's the first qualifier. We're not peaking yet. We got the three points."