You need to adjust your pitch to keep the speed fixed during the climbout. Below the thrust reduction altitude the power will remain constant, so you have to increase your pitch to prevent additional acceleration.
If you arm VNAV before takeoff this will engage and set the increased speeds as you pass the thrust reduction altitude based on your flap position, and as a result the flight director will be providing you pitch guidance to remain at these speeds. All of this is independent of the autopilot.
Kevin Roche