Footage emerged online of fans being hit with truncheons and being shot at with rubber bullets by the heavy-handed policing.
Twitter account @FACKilltheBill, which campaigned to have the Offensive Behaviour at Football Act repealed, uploaded two videos of Celtic fans being harassed and attacked by officers.
They tweeted: “Some appalling footage appearing tonight showing Spanish police violently attacking supporters without provocation in Valencia. We urge all fans to stay safe, and if necessary to document any abuses, especially if arrests are made.”
And later posted: “Spanish police now firing rubber bullets at crowds of Celtic supporters. Despicable beyond description. We urge all fans to stay safe. This clip will disgust any right minded person.”
Another video showed a fan lying on the ground outside a pub surrounded by officers.
Scott Tobin, who posted the clip on Twitter, said: “Police went nuts for nothing at st Patrick’s, smashing people with batons wtf!! Old man got the s**t kicked out him.”
The authorities were expecting around 10,000 Celtic fans to travel for the Europa League last-32 clash with Brendan Rodgers’ side trailing 2-0 from the first leg. The club’s 2,500 allocation has been sold out.
The game was categorised as “high risk” by the Spanish government’s Anti-Violence Commission.
It is not the first time British football fans have clashed with Spanish police with Premier League clubs from England witnessing their fans being attacked when supporting their side in Champions League or Europa League action.