The 20-year-old Brazilian has had a frustrating first season at Inter, making just nine appearances, all as a substitute, and playing a total of only 111 minutes since his 30 million euros (25.94 million pounds) move from Santos last August.
He has managed one goal and picked up three yellow cards in that short period on the pitch.
His frustration boiled over during the 3-1 win at Lazio after he was not among the three substitutes brought on by coach Stefano Vecchi in the closing minutes of the game.
Television pictures showed him angrily leaving the bench before the final whistle.
"Inter supporters and team mates, during yesterday's game I suddenly adopted a thoughtless and inadequate attitude by leaving the pitch before the end of the game," he said on his Facebook page.
"Once the heat of the moment had died down, I realised, in calmness and with the support of my family, that the incident was unsporting and contradicted my professional values.
"I recognise my mistake and would like to register my sincere apologies to all the Inter fans who always supported me and to my team mates."
Gabriel, whose made his professional debut as a 16-year-old in 2013, emerged as one of Brazil's great hopes during three seasons at Pele's former club as he scored 57 goals and impressed with his pace, trickery, skill and clinical finishing.
He scored on his Brazil debut against Panama last year, went on to play at the Copa Centenario and won Olympic gold in Rio de Janeiro with the under-23 team.
Vecchi said after the game that he expected the club to take action, although Inter have not commented since.
(Writing by Brian Homewood; Editing by Ken Ferris)
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