Yes, a lower retirement age causes lower economic productivity because there are less workers in the workforce. As long as a person over the current retirement age is capable of working, their labor only adds to the available labor in the workforce, instead of having them prematurely removed from the workforce.
Raising the retirement age would be an unfair non-solution to economic problems. Many people work physically demanding jobs and they cannot work as long as people in white collar jobs can. Pushing back the retirement age would put more of the burden on these physical laborers who are probably already making less money than the older employees of a law firm or accounting firm who can easily work into their 70s.