Evans has performed 28 Davis Cup ties for Nice Britain and was a substitute after they gained their final title in 2015.
Nevertheless, he was swept apart within the first set by Shapovalov, who silenced the 15,000-strong crowd at Manchester Area by taking the opener in simply 25 minutes.
The Briton, 34, lastly received on the scoreboard when he held early within the second set however did not profit from two break factors at 4-4.
Former world quantity 10 Shapovalov was capable of again up a dominant first set when he struck the decisive blow at 6-5 to take his nation to the knockout phases, which can happen from 19-24 November.
Evans stated afterwards he would converse to captain Smith about doubtlessly ending his Davis Cup profession.
“I’ve considered it lengthy and exhausting. I am going to need to suppose a bit extra,” Evans informed BBC Sport.
“I really like competing for my nation. I’ve cherished each minute of it however generally you have to know when to depart.
“It will likely be a troublesome determination however generally it is good to offer someone else the chance and watch from afar.”