"It is important for the club to find a balance in a world driven by economic and political needs. This club usually does that," Houllier said.
"The club needs to consider its roots and understand that it can't always have a quick fix."
The £65m bid for a 30% share in the club by Thai Prime Minister Thaksin Shinawatra has increased the pressure to challenge for honours.
"I would have been extremely happy to carry on my job," added Houllier. "I wanted to and intended to.
"The reason we have agreed to part company is because of the sudden excessive pressure on the board and myself.
"The pressure, I can cope with, but I thought it could have been harmful for the players in next season's campaign.
"I thought it could jeopardise their performance and achievement and that's why we agreed to come to this situation. I have always said the club comes first."