Henry was widely criticised by the club's supporters after Liverpool failed to sign Clint Dempsey from Fulham and failed to sign a replacement for Andy Carroll.
Manager Brendan Rodgers has also revealed that he would not have let Carroll leave the club on loan if he knew he was unable to add to his squad, which has prompted the statement from Henry.
Henry said: "We will never place the club in the precarious position that we found it in when he took over at Anfield.
"We will invest to succeed but will not mortgage the future with risky spending.
"We are still in the process of reversing the errors of previous regimes.
"I am as disappointed as anyone on this occasion that we were unable to conclude acceptable deals."
Liverpool suffered a 2-0 defeat to Arsenal on Sunday to leave them with just one point from their opening three Premier League games.