The Netherlands international joined Arsenal's Premier League rivals Manchester United, where he has scored seven goals in eight competitive appearances so far this season.
"I thought Robin was a mistake," Adams told the BBC. "I think he could have played for four or five more years.
"I hope they do go on and win everything. Realistically, I think they will fall short again. I wouldn't have made that decision [to sell Van Persie].
"Because I do believe if you want to win major trophies you need [the] best players."
Adams played for Arsenal between 1983 and 2002 and won the English first division title on four occasions and the FA Cup thrice.