That depends on whether you have a gain on the sale and how much depreciation was taken. The depreciation both reduces your basis and can result in ordinary income. 

Because this was a rental property, you are required to reduce your basis in the property by the amount of depreciation that was taken, or allowed to be taken, while your property was a rental. 

In addition, the amount of gain that is due to depreciation taken, is not capital gain, it is ordinary gain and taxed at your regular tax rate.

Here is an example:

Property purchase price                     $100,000

Depreciation taken over 10 years     -  $35,000 

Adjusted basis of property                     $65,000

Sales price                                            $110,000

Adjusted basis                                   -  $65,000

Total gain                                               $45,000

Total gain                                              $45,000

Ordinary gain                                        $35,000

Long term capital gain                          $10,000

I don't owe capital gains tax on home sale due to exclusion (4 years as a rental).

How long it was a rental is irrelevant. It could have been a rental for 50 years and still qualify for the capital gains tax exclusion. The requirement for the exclusion is that the property must have been your primary residence for at least 2 of the last 5 years you owned it, counting back from the closing date of the sale. More specifically, 24 months of the last 60 months you owned it, and the 24 months do not have to be consecutive.

Do I still owe for depreciation recapture?

Yes. Depreciation is not excluded from taxation. If you sold the property at a gain, you will pay taxes on the recaptured deprecation no matter what. No exceptions.

Did you move for a qualifying reason?  Four years of rental implies you DO owe capital gains (in addition to the tax based on the gain due to depreciation) unless you moved for a qualifying reason.