Liverpool principal owner John Henry has released a statement expressing his "disappointment" at the failure to add to their strike force in the summer transfer window.
However, he defended the club’s transfer policy, saying: “We will never place this club in the precarious position that we found it in when we took over at Anfield.”
Arsenal's 2-0 win at Anfield yesterday condemned the Reds to their worst start since the 1962-63 season.
Rodgers’ team head into the international break in the relegation zone and, after a disastrous final two days of the transfer window when they allowed Andy Carroll to join West Ham before failing to secure the anticipated replacement, major questions are suddenly being asked of the Merseysiders’ new boss.
Mr Henry has said the club's inability to add further to their strike force in this summer transfer window was not through any lack of desire or effort.
In his letter Mr Henry said: "They pushed hard in the final days of the transfer window on a number of forward targets and it is unfortunate that on this occasion we were unable to conclude acceptable deals to bring those targets in.
"But a summer window which brought in three young, but significantly talented starters in Joe Allen, Nuri Sahin and Fabio Borini as well as two exciting young potential stars of the future - Samed Yesil and Oussama Assaidi - could hardly be deemed a failure as we build for the future.
"Nor should anyone minimise the importance of keeping our best players during this window. We successfully retained Daniel Agger, Martin Skrtel and Luis Suarez. We greatly appreciate their faith and belief in the club. And we successfully negotiated new, long-term contracts with Luis and with Martin."
The American owner reaffirmed his commitment to the club.
He said: "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.
"The transfer policy was not about cutting costs. It was - and will be in the future - about getting maximum value for what is spent so that we can build quality and depth. We are avowed proponents of UEFA's Financial Fair Play agenda that was this week reiterated by Mr Platini - something we heartily applaud.
"We must comply with Financial Fair Play guidelines that ensure spending is tied to income. We have been successful in improving the commercial side of the club and the monies generated going forward will give us greater spending power in the coming years."
Mr Henry went on to say they are still in the process of reversing the errors of previous regimes.
"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.
"Spending is not merely about buying talent. Our ambitions do not lie in cementing a mid-table place with expensive, short-term quick fixes that will only contribute for a couple of years. Our emphasis will be on developing our own players using the skills of an increasingly impressive coaching team. Much thought and investment already have gone into developing a self-sustaining pool of youngsters imbued in the club's traditions.
"That ethos is to win. We will invest to succeed. But we will not mortgage the future with risky spending.
"After almost two years at Anfield, we are close to having the system we need in place. The transfer window may not have been perfect but we are not just looking at the next 16 weeks until we can buy again: we are looking at the next 16 years and beyond. These are the first steps in restoring one of the world's great clubs to its proper status.
"It will not be easy, it will not be perfect, but there is a clear vision at work.
"We will build and grow from within, buy prudently and cleverly and never again waste resources on inflated transfer fees and unrealistic wages. We have no fear of spending and competing with the very best but we will not overpay for players.
"We will never place this club in the precarious position that we found it in when we took over at Anfield. This club should never again run up debts that threaten its existence.
"Most of all, we want to win. That ambition drives every decision. It is the Liverpool way. We can and will generate the revenues to achieve that aim. There will be short-term setbacks from time to time, but we believe we have the right people in place to bring more glory to Anfield.
"Finally, I can say with authority that our ownership is not about profit. Contrary to popular opinion, owners rarely get involved in sports in order to generate cash. They generally get involved with a club in order to compete and work for the benefit of their club. It's often difficult. In our case we work every day in order to generate revenues to improve the club. We have only one driving ambition at Liverpool and that is the quest to win the Premier League playing the kind of football our supporters want to see. That will only occur if we do absolutely the right things to build the club in a way that makes sense for supporters, for us and for those who will follow us. We will deliver what every long-term supporter of Liverpool Football Club aches for."