I came across the above quote, and found it quite interesting. However, I struggled to find an actual source. Did Newton truly say this?
So far I have been unable to find substantially identical words in Newton's writings, and as usual, authors that use this quotation do not cite a source. The origin may be a remark of Newton's in private correspondence which was embellished over time.
In a letter from Isaac Newton to Richard Bentley, dated December 10, 1692, apparently in the context of his work on gravity, he wrote:
But if I have done the publick any service this way 'tis due to nothing but industry & a patient thought.
Thomas Reid, Essays on the Active Powers of Man. Edinburgh: John Bell 1788, p. 80:
Sir Isaac Newton, to one who complimented him upon the force of genius, which had made such improvements in mathematics and natural philosophy, is said to have made this reply, which was both modest and judicious, That if he had made any improvements in those sciences it was owing more to patient attention than to any other talent.
Some authors claim that the person who had complimented Newton was Dr. Pemberton. This is presumably Henry Pemberton (1694 – 1771). While Pemberton knew Newton personally and later wrote a book on Newton's philosophy, I have not been able to identify anything relevant to the question in Pemberton's publications.
Tryon Edwards, A Dictionary of Thoughts; Being a Cyclopedia of Laconic Quotations. New York: Cassell 1891, p. 120:
If I have ever made any valuable discoveries, it has been owing more to patient attention, than to any other talent. — Sir Isaac Newton.
Here we have a version substantially identical to the one from the question in a reference work that may have enjoyed wide circulation.