In the letter obtained Thursday by The Associated Press, Alisher Usmanov and Farhad Moshiri wrote to Kroenke expressing "deep reservations" about how he runs the club after captain Robin van Persie declined to sign a new contract.
Usmanov and Moshiri own just under 30 per cent of Arsenal through investment company Red & White, but they haven't been allowed by Kroenke to join the board.
They complain in the letter that Kroenke is running Arsenal "without any investment" and with little sign that a trophy drought stretching back to 2005 will end soon.
"It is down to our manager and not the shareholders to have to deal with the club's tight finances, carry the burden of repaying the stadium debt by selling his best players and having to continue to find cheaper replacements," Usmanov and Moshiri wrote. "All of that, naturally, comes at the expense of performance on the pitch.
"This policy is leading to the loss of our best players, often to our main competitors, and even causes the players themselves to question their future at the club and the club's ambitions. The situation with our captain and outstanding performer from last season, Robin van Persie, sums this up."
Van Persie announced in a shock statement on Wednesday that he would not extend his Arsenal contract, which expires in a year, because "we in many aspects disagree on the way Arsenal should move forward."
The Netherlands forward scored 37 goals in all competitions for Arsenal last season.
"Yet again we are faced with losing our true marquee player at the club because we cannot assure him of the future direction and give confidence that we can win trophies," Usmanov and Moshiri wrote. "Where are the safeguards to ensure that this doesn't happen again and again in the future?"
Arsenal has lost other stars in recent years amid dissatisfaction about the lack of success and lack of funds for transfers. A year ago, then-captain Cesc Fabregas joined Barcelona, while playmaker Samir Nasri and defender Gael Clichy signed for Manchester City and won the Premier League title in May. City also recruited Emmanuel Adebayor and Kolo Toure from Arsenal in 2009.
"As a top club we should, at the very least, match if not beat the offers that other clubs make to try and lure our very best players away, and also provide a more compelling vision of the future," Usmanov and Moshiri wrote.
"You can try and put a good face on a bad game for as long as you want, pontificating about the merits of this model, but it will not hide the obvious fact that it just does not allow our great manager to fully realize his managerial talent and deliver success for the fans who are paying the highest prices in the land."
Usmanov and Moshiri complain to Kroenke and other board members that it seems securing a place in the Champions League "will be the pinnacle of our ambition again next season."
"Unfortunately, in the future we may see this ambition lowered further," they added.
Usmanov and Moshiri say they have been refused meetings with Kroenke, who has just completed his first season in charge of Arsenal in which the team finished third in the league standings.