Immobile went down under a challenge from Vidal, who bent down over his opponent and Immobile appeared to prod the Chilean who reacted theatrically.
Speaking after the match, Lazio boss Simone Inzaghi defended his striker, when he said: "He was provoked. We are sorry because we could have done more if he had been there for the whole of the match.
"More than the result I am happy with way the lads came through this test, they showed great heart. It was an emergency situation and we reacted well to three injuries and Immobile's sending-off."
Antonio Conte's side went ahead with one of the first chances of the match as Ivan Perisic tried to squeeze between two defenders and the ball ran loose to Martinez, who turned it in from 12 metres.
The match degenerated after that although Marcelo Brozovic nearly snatched a winner for Inter with a shot which was deflected onto the post.
Inter coach Antonio Conte said he was was left frustrated by result, saying: "That's football, We had desire and played with sacrifice and we felt we had the three points within our grasp.
"We conceded a goal during our best moment of the game, when we were dominating. But I was pleased with the performance, we played football with personality. We have to keep working."
"It's still a good result," he added. "Last year, we dropped all three points here."