Having been frustrated for nearly the entire game, Coutinho poked the ball past Costa Rican goalkeeper Keylor Navas one minute into stoppage time before Neymar's volley wrapped up the points for a relieved Brazil.
His first touch took the ball away from the defender and Coutinho raced in to poke it through the legs of Keylor Navas from six metres out and claim his second goal of the tournament.
"If I was the referee I wouldn't go back on my decision but I respect that because it's subject to interpretation", said the 57-year-old.
The striker was sidelined for three months after a foot injury in February required him to undergo surgery.
Brazil were not just unhappy with the treatment meted out to Neymar, but also Switzerland's equaliser when the Video Assistant Referee (VAR) system failed to rule out Steven Zuber's equaliser for a slight push on Miranda.
Tite said he thought his superstar's tears were down to the huge pressure of leading the five-times world champions. I think he has [been criticised].
Moments after Coutinho's goal, Neymar got a goal of his own to give a Brazil a 2-0 win over Costa Rica at Saint Petersburg Stadium.
"He's a human being, he needs some time to resume his high standard". "Today [Friday] he disappointed me, because he insulted me really badly when I returned the ball".
Brazil outshot Costa Rica 23 to 4 over the course of the match with nine on target to zero for the CONCACAF squad.
Neymar wrote: "Not everyone knows what I've come through to get here".
Ahmed is an ardent fan of Neymar Jr and the Brazilian football team.
"Costa Rica is a team with a lot of quality, strong in defence and midfield, and the most important thing for us was not giving up until the last minute".
Brazil are now on four points and top Group E, with Serbia (2nd) set to play Switzerland (3rd), while Costa Rica are the first CONCACAF nation to exit the World Cup.
Navas pulled off a spectacular save in the second half to deny Neymar from close range, as the game opened up. Firmino drove through the middle before Douglas Costa squared for Neymar finally to find the net.