Brazil head coach Tite claimed Steven Zuber pushed his marker before netting Switzerland's equaliser in the 1-1 World Cup Group E draw but said he was glad the defender did not go to ground.
Miranda alleged the Swiss midfielder pushed him in the back before he leaped to score with a header that cancelled out Philippe Coutinho's first-half strike for Brazil, and Tite agreed that a foul should have been given.
After missing a number of late chances to win the game, Brazil were forced to settle for a draw from their opening match of the tournament and Tite was disappointed with their finishing.
When asked whether VAR should have been used to check the legality of the equaliser and of a second-half challenge on Gabriel Jesus by Manuel Akanji, Tite said: "I don't want to make excuses. You don't have to put pressure on the referee – there is a whole system in place, people are assessing the game.
"The Miranda moment was very clear. The second play you can interpret but the first one you can't discuss - the people responsible for that must work within fairness. You have to be fair.
"If they push the player, what can I say? There was a foul there.
"I spoke to Miranda and he said, 'When he pushed me I should have fallen' and I said: 'No! Absolutely do not do that, otherwise it's a simulation of the foul. Do not simulate anything.'
"It's the player's responsibility. I said to him: 'Don't fall, don't draw a foul'."
Brazil had 21 shots on goal of which only five were on target, compared to Switzerland's six attempts of which two were goal-bound.
Tite admitted that the pressure of the occasion may have made his players anxious in front of goal.
"There was a lot of pressure but we couldn't translate it into a precise finish," he said.
"As you speed up, your last move becomes imprecise. We had too many balls off target. We could have made their goalkeeper work a little more given the number of chances we had.
"We could have been more precise in our finishing. It's a kind of anxiety, wanting to win, wanting to really do it."