Evans has performed 28 Davis Cup ties for Nice Britain and was a substitute once they received 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 Enviornment by taking the opener in simply 25 minutes.
The Briton, 34, lastly obtained on the scoreboard when he held early within the second set however didn’t benefit 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 is able to happen from 19-24 November.
“I’ve considered it lengthy and exhausting. I am going to must assume somewhat extra,” Evans advised BBC Sport.
“I like competing for my nation. I’ve liked each minute of it however generally you have to know when to go away.
“Will probably be a tough resolution however generally it is good to present anyone else the chance and watch from afar.”
Evans has dropped to 178th on this planet rankings after opting to overlook some tournaments this 12 months to give attention to taking part in doubles on the Paris Olympics with Andy Murray.
“His rating has gone down so he is obtained a whole lot of issues to think about – what’s greatest for him proper now and what does he must have a profitable 12 months subsequent 12 months,” Smith advised BBC Sport.
“No matter occurs, he is been an incredible servant for us.”
