The US dominated play for long periods but were unable to convert a flurry of first-half chances and played out a second straight draw, after Monday's 1-1 stalemate with Wales.
Berhalter's side are third in Group B with two points and would go through to the last 16 for the fifth time since 1994 with a win over Iran in their final group game on Tuesday.
"The final product still could be better... I'm overall pleased with the performance of the group, most importantly the belief of this group because that never wavered," Berhalter told reporters.
"What I saw pre-game was a team that was extremely focused on getting results. In the end, it sets up our first knockout game of this World Cup and that's going to be a focus of ours.
"We played with a ton of spirit but we're going to have to be up for it (against Iran). We want a chance to advance... We know it's going to be a difficult game, and I'm looking forward to the opportunity."
Tyler Adams, Yunus Musah and Weston McKennie ran the show in midfield and the Americans were unlucky not to be ahead at the break, with Christian Pulisic rattling the crossbar with a fierce left-footed strike.
England, who crushed Iran 6-2 in their group opener, were outplayed by the vibrant albeit inexperienced Americans, who returned to the World Cup stage after eight years, and were loudly jeered by their supporters at the final whistle.
"I guess that's a positive sign when you play for the other team," Chelsea forward Pulisic said. "It was a really solid performance from the team against a good opponent.
"We were a team out there who showed a lot of confidence and battled toe-to-toe... but the job's not even close to done so we've got a lot of work to do."
