Messi's mesmeric run and strike ranks as one of the finest goals of the tournament so far, but the Argentina captain admitted he was relieved the team had secured a 2-1 win in the Maracanã after an insipid first-half.
Sead Kolašinac deflected the ball into his own net in the third minute before Messi scored a stunning second after a superb run to make it 2-0.
Substitute Vedad Ibišević grabbed a late goal for Bosnia and Messi conceded the evening was a nervy affair for his team.
"It's important that we started off on the right foot with the three points, but we do have things we must improve," Messi said. "It's not easy with all the anxiety and the nerves, but the important thing is the result. We had a great second half. We had the ball much more, created several opportunities and that's what we have to continue to do."
Argentina coach Alejandro Sabella awarded his team an accurate mark of six out of 10 and said his half-time changes to provide more support to Messi had been crucial.
Sabella said: "On balance I would give it a six. We need to improve and part of that is in my hands - it is up to me.
"The changes at half-time just produced this improvement. They were playing better together and there was more support around Messi. Once Messi received the ball there was better follow-up and better support.
"I think that, whatever happens in this World Cup, he is among the best players in the history of football."