Messi set up Cristian Tello for all three of his goals as Barcelona overcame their first-half struggles with a blistering performance in Valencia on Wednesday.
The head coach admitted his side had been out of sorts in the first half and were lucky that a Juanfran own goal cancelled out Nabil El Zhar's opener, before Tello hit his hat-trick.
"It's true we played really well in the second half and not in the first, when we didn't have enough penetration," Martino said.
"To be honest, we lacked more mobility and a bit of everything, and we made a mistake in conceding a goal but we could recover after that.
"We were struggling to score and then we were lucky with Levante's own goal and could draw level.
"After that, we could see the best performance of the team.
"When (Lionel) Messi participates like today he can change any game.
"Leo is one of our players who can change these kind of games - he didn't score today but gave three key assists to Cristian (Tello) and we could revert the score.
"He always appears when we need him to turn the games and that's something we have to consider."
Barcelona host Malaga in La Liga on Sunday, attempting to maintain their top position in the standings, before welcoming Levante for the second leg of the Copa del Rey tie next week.
