They were eliminated in round 2 of the National Westminster Bank Trophy and at group level in the Benson & Hedges Cup.
Kim Barnett scored five centuries in the first class game and two in one-day events to make him top scorer.
Derbyshire had six wins in the championship but ended twelfth as on several occasions Barnett chose to make a (losing) game of it rather than playing for a draw.
Dominic Cork made his debut for the club playing one match in what was to be the first of many seasons.
Derbyshire also played a one-day match against the Indians at Queen's Park, Chesterfield on 16 Jul 1990, which India won by two wickets.