It was just what Zola had demanded from his players, who survived an uncomfortable first half-hour before making their move.
He said: "It was the result we were looking for and we are pleased.
"It wasn't, especially in the second half, a brilliant performance, but maybe we thought we wanted to keep it that way and not risk too much.
"But it was a great result. That's what we wanted and it was very professional."
If the game turned on Behrami's 44th-minute strike, Pool's hopes of staging a fightback were killed in their infancy when, in injury time at the end of the first half, referee Lee Mason's controversial penalty decision handed the Hammers a second, decisive goal.
Central defender Michael Nelson, for reasons best known to himself, handled Carlton Cole's flick-on, and the official pointed to the spot, although replays confirmed the incident had taken place at least a yard outside the penalty area.
Mark Noble, however, was not distracted by the boos ringing around Victoria Park and duly dispatched the ball past keeper Arran Lee-Barrett to secure the victory.
Zola said: "I haven't seen it. They have just been telling me now. It might be, I don't know.
"But sometimes in football, the referee can pick up a right decision, sometimes they can be wrong. But I don't think we beat Hartlepool because of that penalty."
Up until Behrami's goal, the League One side had more than made a fist of it, and had the impressive Scott Parker not cleared Michael Mackay's ninth-minute header off the line, things might have been even more uncomfortable for the visitors.
Robert Green had to make a fine one-handed save from Gary Liddle's header after the break, but by that point Pool's cause was a lost one.
Pool's director of sport Chris Turner, however, was not making excuses.
He said: "I'm not going to harp on about that decision. It went against us.
"I wasn't complaining at the time, but if it's not in the box, it's not in the box. But that's life.
"That second goal made it a lot easier for West Ham to come out in the second half and play how they played, and made it a lot harder for our boys going out in the second half because it was a mountain to climb psychologically.
"But in both halves of the game, the first 25 minutes of each half, we took the game to West Ham, caused them problems and put in a very creditable performance."
The win extended West Ham's unbeaten run to six games and left Zola, twice an FA Cup winner as a player with Chelsea, dreaming of another trip to Wembley.
He said: "To be fair, the players were really focused. They want to go to Wembley - we want to go to Wembley, and to go there, we need to go through games like this."
Meanwhile, Zola was unable to report any progress on the club's efforts to replace striker Craig Bellamy following his £14million move to Manchester City, but he insisted defender Matthew Upson is going nowhere.
Asked if Upson will remain at Upton Park, the Italian said: "Definitely. Matthew Upson didn't play today because he has played so many games and he needed a rest.
"He has also got some internationals coming up, so he needed to have a rest and I decided it was the time to rest him."