The pressure was on Argentina to make a winning start in Brazil and they did, with an early Sead Kolasinac own goal and Lionel Messi's second-half effort helping the South Americans to a 2-1 win in Group F action at the iconic Maracana.
Despite running out winners, Argentina were far from their best against the World Cup debutants in Rio de Janeiro, but a relieved Sabella said his team would be 'cherishing' the result.
"It was an even game right from the start, though the second half was a little more entertaining," Sabella told reporters post-game.
"We started to make more chances when (Gonzalo) Higuain came on and we got the second goal, which helped us settle down.
"I can't really have any complaints about the result. Perhaps we made an error or two, and I'm sure I got one or two things wrong.
"But we should cherish these three points because the Bosnians were no pushovers."
Messi put Argentina two goals in front with 25 minutes remaining before Bosnia-Herzegovina substitute Vedad Ibisevic set up a nervy finish after pulling a goal back six minutes from time.
The Argentina captain admitted his team-mates had experienced nerves as they look to live up their tag as World Cup favourites, while he also called for improvement.
"It's only normal to feel a little bit anxious and nervous in the first game," said Messi, who netted his second-ever World Cup goal. "The main thing is just to get the win.
"We made more chances in the second half, and though there are some things we need to work on, what matters are the three points."