Simple answer: No.
The capital gain on the sale of your primary home is not taxable (up to $250K, $500K married). To be eligible you must have lived in and owned the home for at least 2 out of the 5 year prior to sale. You do not even need to report it on your tax return, unless you got a tax document, usually a 1099-S. The 1099-S may have been included in your closing documents, instead of arriving in the mail, in Jan. or Feb. of the following year.
The fact that you will not reinvest the profit in a new home does not change that (that's an old rule that went out in 1997).