The Falcon 9 first stage uses 3 engine burns in its landing trajectory:
Boostback, to kill its forward velocity and return in the general direction of the landing pad. This decelerates the stage from 5000 km/h to 0, plus a bit of return speed.
Reentry, to reduce its speed as it enters the atmosphere. Starts at 45 km up, the stage is supersonic at the start of this burn.
Landing, to steer the stage toward the landing pad and kill off its remaining speed. Note: if the engine fails at this stage, the current trajectory will have the rocket crash into the ocean.
So, how much remaining speed are we talking about?
According to the post-landing teleconference, the sonic booms arrived at a point 4 miles from the landing pad at about the same time that the rocket landed. Taking a few shortcuts, that means the booms originated 20 seconds before landing, or well into the landing burn (which started 30 s before landing). So the landing burn starts at a speed of 400-500 m/s.
Now, if you want to replace just the landing burn with a parachute, you'll have to do something about that initial speed. Parachutes that work at supersonic speeds are rare: the only ones I know of have been built for Mars, not Earth. So you need to extend the reentry burn to decelerate the stage to something like 150 m/s.
You'd also need just about the largest parachute ever built to decelerate the 23-ton stage. This parachute weighs about 1 ton.
So instead of a rocket burn with a delta-V of 500 m/s, you get a rocket burn with a delta-V of 350 m/s (1) plus a deployment of the largest parachute ever made, plus another rocket burn to cushion the landing.
This seems to add a lot of complication for little benefit, especially when you add in the fact that you also need to steer that parachute because your existing steering mechanism (rocket nozzle plus grid fins) don't work anymore when you're under a parachute.
You've also inserted more points of failure into the system.
Finally, parachutes add a lot of work to refurbishing the rocket: they have to be inspected, carefully packed etc. And they add complexity to the landing: say the rocket lands on a barge in the ocean. The rocket's upright, but the parachutes float down into the water where they quickly fill up and start pulling the top of the rocket sideways, threatening to tip it over. You'd have to have a quick and foolproof way of disconnecting the parachute from the rocket while not letting it sink to the bottom of the ocean. Remember the barge is unmanned during the landing so this would have to be done automatically.
1: assuming the rocket speed at the end of the reentry burn is 500 m/s