Alonso became F1's youngest double world champion by 2006, but since then has failed to win another title with Renault, McLaren and Ferrari.
"Fernando Alonso has had the chance to win up to five world championships, but the reality is that there is always a mess wherever he is," the Brazilian, whose son Nelson Jr was Alonso's teammate in 2008, told La Sexta.
"He is a fantastic driver, but also one who generates a lot of problems and in the end everyone ends up leaving the team.
"He is very bad politically in his work on the team. When you arrive on a team, at first you must be patient and work together, and later you win.
"But he always wants the best [straight away], and that is not the best way."
Asked to compare Alonso with new quadruple world champion Lewis Hamilton, the 65-year-old answered: "I do not think Alonso is better. I think they are at the same level."
Piquet retired a three-time world champion in 1991.