Gazidis highlighted what he termed the "invidious" involvement of some agents in transfer dealings and believes players should be taking more money themselves from the deals, rather than it going to agents.
Gazidis did not spell out specific conflicts of interest but these could include agents working for both players and clubs, or working for both a manager and a player at the same club.
The Arsenal chief was speaking at a press conference following the European Clubs' Association general assembly in Barcelona.
Gazidis said: "Clearly there is a lot of money going to agents in these transfer transactions but I don't think we the clubs can abrogate responsibility - we are part of the problem as we are the ones agreeing to pay these amounts of money.
"There are unusual pressures in the system which lead to agents having significant leverage. Players should be making more money and that money not going to agents."
He added: "If I were a player or players' union that would be a really substantial concern to me because it means my clients as a union and me as a player are losing money.
"More invidious are conflicts of interest that often exist in these transactions with agents, and that's something that clubs and players should be concerned about."
Research by the ECA has flagged up that 14.6 per cent of all money paid in transfers ended up going to agents.
Gazidis added: "Clearly there's a lot of money going to agents and we, as clubs, are part of the problem but there are some unusual pressures in the system particularly when you are dealing across jurisdictions, that means agents have a significant degree of leverage."
A study commissioned by the ECA also found many clubs are failing to pay other teams enough compensation for training players they sign.
According to FIFA's transfer rules, five per cent of transfer fees should be paid to the teams that trained the players between the ages of 12 and 23 but nearly 200m million US dollars (£120million) was not paid out.
Clubs in Africa and South America who were unaware they could be due money were the ones most likely to have missed out, according to the report.