I disagree. Communists LOVE innovation, especially when they can tout it as part of the superiority of their system. However, the system is antithetical to human nature in that it removes most rewards for competition (no ability to get patents, or profit from your innovation), so innovation tends to slow to a trickle. In other words, it is not an explicit feature of the system, but rather a huge bug.
The exception seems to be when there is EXTERNAL competition, such as in the case of the USA/USSR space race. Here, competitive human nature is awakened and progress is made.