"(Amazon is) investing in areas where there are shortages of capability in markets and if we don't have the capability … or if a competitors of ours doesn't have it, they're going to put it in to serve their customers," McCullough told CNBC's "Managing Asia."
UPS has worked with Amazon since the internet company first started doing business, but it's also important for UPS to be "upfront" with what it can and cannot do for its customers, McCullough added.
"I've had the benefit of being around Amazon since 1996 so I've seen them evolve — nothing short of impressive. They're investing in areas where there are shortages of capability in markets … They have to do what they have to do," McCullough said.
Amazon has made the push into last mile delivery, or the transportation of goods from a delivery hub to the end destination in the supply chain, in a bid to drive profit margins down further. One of these strategies has been the use of drone delivery services, which the internet company successfully pulled off in December.
The e-commerce company's investments in infrastructure might be making delivery more affordable to attract retailers looking for cheaper logistics options, but McCullough appeared unfazed.
"Free shipping has been around, again, since 1996. I used to run an e-commerce team and … there's no such thing as free shipping," McCullough said.
"It takes money to hire and build these great buildings, (to) make sure that technology and infrastructure is in place. So the question for us is, can we do this every day, worldwide? … Certainly, the notion of free and who's consuming the cost associated with 'free' is going to be an ongoing battle," he added.
Costs will continue to remain a core focus for UPS, as it attempts to drive costs down while improving densities, or the volume of packages per delivery stop made. This will improve the economics of a single stop, McCullough said.
"As a UPS-er, we have a phrase called 'constructively dissatisfied.' We're never satisfied, ever," McCullough said.
More From CNBC