Henry's Fenway Sports Group (FSG) came under fire for the decision to loan England striker Andy Carroll to West Ham United without signing a replacement by Friday's summer transfer window deadline day and the poor start has led to further complaints.
Responding to the criticism, the principal owner said it was "not through any lack of desire or effort" that the club had failed to sharpen their attack in a period which has garnered only one point from three league matches.
"I am as disappointed as anyone connected with Liverpool Football Club that we were unable to add further to our strike-force in this summer transfer window," he wrote in the letter published on the club website.
"It is unfortunate that on this occasion we were unable to conclude acceptable deals to bring those targets in. No one should doubt our commitment to the club.
"In Brendan Rodgers, we have a talented young manager and we have valued highly his judgement about the make-up of the squad.
"This is a work in progress. It will take time for Brendan to instill his philosophy into the squad and build exactly what he needs for the long term."
Henry added that Liverpool were continuing to pay the price for the failings of the previous regime after bringing to an end the acrimonious reign of fellow Americans Tom Hicks and George Giller with their Anfield takeover in October 2010.
"We are still in the process of reversing the errors of previous regimes," he said. "It will not happen overnight. It has been compounded by our own mistakes in a difficult first two years of ownership.
"It has been a harsh education, but make no mistake, the club is healthier today than when we took over."
Writing in Britain's Daily Telegraph on Monday, former Liverpool defender Alan Hansen blamed FSG for the "debacle" which has left the side woefully short of attacking options.
"By sanctioning the departure of Andy Carroll and then failing to come up with the money to sign Clint Dempsey, Liverpool's owners have left manager Brendan Rodgers in the lurch," Hansen said.
"Liverpool are desperate, but they only have themselves to blame because they got rid of a striker - a £35 million England international at that - and failed to replace him."
Rodgers cut a forlorn figure at Anfield on Sunday after admitting he would not have let Carroll go if he had known there were no reinforcements on the way.
TRANSFER DEBACLE
Despite FSG's determination to reduce the club's inflated wage bill, many fans and experts were dismayed at Liverpool's ineptitude as the transfer deadline closed on Friday.
"It is all very well having a philosophy, but one of the golden rules in football is that you don't let somebody go until you have brought somebody else in," Hansen added.
"Whether it was the right or wrong decision, Carroll was allowed to join West Ham last Thursday," he added, suggesting it was also tactically wrong to let the big centre-forward go.
