Videos taken at the time show stewards striking Spurs fans with batons inside and outside the stadium, injuring several travelling supporters.
Tottenham are worried that the fine will not deter a repeat of the incident.
“The safety and wellbeing of our supporters is paramount to the club when traveling both domestically and overseas,” a club spokesman said, as reported by The Daily Mail.
“The treatment our supporters received in Barcelona some six months ago was completely unacceptable, something UEFA has acknowledged, and some are still recovering as a result of this ordeal.
“We went to great lengths, along with Tottenham Hotspur Supporters’ Trust, to gather evidence so UEFA could take appropriate action. We thank them for assisting us in gathering the necessary information.
“No visiting supporters should have to experience what our fans went through that night again. We have grave concerns, however, that the punishment imposed will not act as enough of a deterrent to avoid a repeat.”
The Supporters’ Trust were even more damning of the sanction, describing it as ‘inconsequential,’ and branding UEFA not fit for purpose.
The group also affirmed that they will be seeking legal advice in their attempts to get justice for the injured fans.
“The fine imposed on Barcelona is less than some of our fans who have been left unable to work as a result of being assaulted will lose in earnings,” the Trust said on Saturday.
“It is twice the amount THFC has been fined for allegedly arriving on the pitch late for a game last month. And it is an inconsequential amount for a club as rich as Barcelona.
“This decision by UEFA sends clear signals. It says supporters are fair game for security staff to do what they want to. It says broadcast rights and kick-off times are more important than supporter safety. And it says UEFA is unfit for purpose.
“We share the grave concerns of our club that the punishment imposed will not act as enough of a deterrent to avoid a repeat. THST will be taking advice, including legal advice, on our next steps.
“We are determined to secure justice for our fans.”