Brazilian football's disciplinary tribunal said Roberto Fernandes lost his temper when the referee signalled five minutes of injury time in the 0-0 draw at Santos on the final day of the season on December 7.
Defeat would have condemned Nautico to relegation.
The tribunal said on its website that Fernandes shouted: "Thief ... I'm going to kill everyone here today. This is a set up against my team".
He then kicked a bucket containing ice and bottles of mineral water and was sent off.
The tribunal also handed relegated Vasco da Gama a one-match home ban and a fine of 10,000 reais ($4,335) after fans threw objects on to the field in a 1-0 defeat by Vitoria which sent them down to the second division.
The referee's report said batteries, a firework, two plastic cups containing an unidentified liquid and empty drink cans were among the objects thrown.
Atletico Paranaense and Flamengo were fined for delays to their game, which Paranaense won 5-3 to stay up.
Paranaense were fined 2,000 reais for taking the field two minutes late for the first half and Flamengo were fined 3,000 reais for an eight-minute delay to the start of the second period.
All nine other matches started on time, a rarity in Brazil where floodlight failures, kit clashes and bus breakdowns are common when decisive matches are due to start simultaneously.
