Messi provided a moment of magic to make it 2-0 in the second half, after an early Sead Kolasinac, but Argentina were made to work hard by the World Cup debutants.
Vedad Ibisevic pulled a goal back for Bosnia six minutes time to give them a chance of claiming a point and, even though Argentina held on, Sabella admitted after the final whistle that Argentina would have to raise their game.
"They were two different halves," Sabella told a news conference.
"In the first one I think we controlled the Bosnians well, but beyond that, we didn't create the kind of depth that we managed in the second half. Obviously we need to improve."
Sabella, who made two changes at half-time, added: "It is true that we failed in parts, in part because of my own mistakes."
Messi echoed Sabella’s view that Argentina would have to improve after a nervy display, but was satisfied to get three points on the board in Group F.
"It was our first game, we are anxious and everything, Bosnia are a good team but we have a to do a lot to improve.
“The good thing is we got the three points and off to a winning start."
Asked about the Argentine fans, who are estimated to have made up around 40,000 to 50,000 of the Maracana crowd, Messi added: "It was impressive. I wasn't expecting anything less, I knew it was going to be like this."
Sergio Aguero admitted that fortune had favoured Argentina, saying: "The game became difficult as we did not have control of the game. Luck helped us today."
Angel Di Maria said: "We knew it was going to be difficult as it was our first game but we got the three points and that was the objective.”