The Spanish side came from behind to secure a 2-1 win over Martin O'Neill's men on Thursday evening, inflicting another damaging European defeat on the Scottish champions.
However, despite the disappointment on the pitch, the occasion appears to have left a lasting impression on the visitors.
Ahead of their La Liga clash with Real Betis, Celtic anthem 'Let The People Sing' was played over the PA system at the Estadio Abanca-Balaídos.
Spanish newspaper Faro de Vigo shared footage of the song echoing around the stadium, writing: "The brotherhood between those from Glasgow and Celta continues three days later in Vigo."
The match against Betis subsequently finished goalless, but the gesture highlighted the growing connection between the two clubs and their supporters.
More than 3,000 Celta fans travelled to Glasgow for Thursday's European encounter, representing the largest away following in the Spanish club's history.
Following their victory at Celtic Park, Celta released an emotional statement reflecting on the experience.
The club wrote: "We're still in shock over what we experienced together in Glasgow. There are things that, no matter how hard we try to explain them with words, can never truly capture their meaning.
"This story began the day we learned our destination, when Glasgow appeared on the European calendar and thousands of Celta fans began to imagine a night that is now part of our history
"More than 3,000 of you crossed Europe to be by our side. You left your homes, your routines, and endured many hours of travel to support the team at Celtic Park.
"You painted Glasgow blue and brought a little piece of Galicia to Scotland, with that unique way we have of turning any place into home.
"For those who have been traveling miles for decades with the badge pinned to their chests and for those who are just now beginning to discover what it means to be a Celta fan.
"Perhaps that's why Glasgow was so special – two clubs united by two fan bases that are proud of where they come from and understand that roots are carried within, but also defended, shared and celebrated.
"This was our biggest away trip ever. A fact that will forever be part of our history. Thank you for being there, for your effort, and for your unique way of showing love for Celta.
"If there's one thing you've shown us again in Glasgow, it's that wherever we are, we never walk alone."
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