The New Saints have alleged striker Aramide Oteh was racially abused following their Champions League qualifying round defeat in North Macedonia.
Saints head coach Craig Harrison said former English Football League player Oteh, 26, was left in tears by the incident with a home supporter.
Shkendija scored a winner late in extra time as TNS were beaten 2-1 in front of a crowd of 3,000 at the Tose Proeski Arena in Skopje.
"The New Saints FC strongly and unequivocally condemn the racist abuse directed at Aramide Oteh by a member of the home crowd following the conclusion of tonight's Uefa Champions League first qualifying round match against KF Shkendija," a statement from the Welsh champions said.
"There is absolutely no place for racism - either in football or in society. Everyone at the club is offering their full support to Aramide and stand firmly by him.
"The New Saints are proud to support UEFA's #NoToRacism campaign and remain committed to promoting equality, respect and inclusion both on and off the pitch."
Englishman Oteh, who came on as a substitute in extra time, joined TNS in 2024 having played for Queens Park Rangers, Bradford City, Stevenage, Salford City, Crawley Town and Walsall.
The London-born player was visibly upset following the Shkendija defeat.
"He is in tears - that doesn't happen for no reason," said Harrison.