Germany went into the game knowing they needed three points to 100 per cent confirm their place in the last-16.
Ozil was recalled to the starting XI after being dropped for the second group match against Sweden on Saturday.
But he and Joachim Low’s side struggled in the first half, going into the break goalless.
Speaking at half time, BBC Sport pundit Jermaine Jenas expected Low to make substitutions early in the second half.
And he suggested Ozil may be one to make way after a poor first half showing.
“I think they will make changes, whether it’s at half time or very soon into the second half,” Jenas said.
“I envisage players like (Ilkay) Gundogan come on the pitch, (Julian) Draxler.
“That’s an easy pass that is from Mesut Ozil as well by the way.
“He’s much better than what we’ve seen there.
“We spoke quite a lot during that first period about the lack of quality and getting into situations.”