Arsenal have sought to avert a row between disgruntled sections of their support and chairman Peter Hill-Wood.
Hill-Wood was quoted in a newspaper as saying supporters critical of the club's lack of trophies in recent seasons were "silly".
But in a statement, Arsenal said: "Emotions can run high in football many times throughout a season. It's because we all care about our club.
"Our fans are at the heart of what we do, and that will always be the case."
Arsenal are still in contention for the Premier League title but face the prospect of a sixth season without any silverware.
They lost to Barcelona over two legs Champions League in the first knockout round of the Champions League, lost the Carling Cup final to Birmingham City and had their FA Cup hopes ended in the sixth round by Manchester United.
But manager Arsene Wenger defended his players on Friday, saying: "Trophies are one way to judge a club... would you swap winning the FA Cup for playing in the Champions League?"
The Daily Star quoted Hill-Wood on Saturday as saying the Arsenal board remained "100% behind" Wenger.
"I simply cannot believe he will react to these stupid comments from these silly people," Hill-Wood said. "They are supposed to be supporters, but, in fact, they do quite a lot of damage.
"We have set the bar high and everybody expects us to achieve that every year, but it simply isn't possible."
Hill-Wood directed his anger towards the Arsenal Supporters Trust who earlier this week expressed "considerable disappointment" at recent results.
The AST meet regularly with the north London club's hierarchy, but Hill-Wood added: "They are in danger of us becoming less friendly with them. We haven't yet, but I am just saying we could become less friendly."
Second-placed Arsenal go into Sunday's match at Blackpool 10 points behind league leaders Manchester United.
The Gunners have two games in hand on the Red Devils but third-place Chelsea are now only a point behind the north Londoners having played one match more.