One of Cook's first duties was to find a successor to Sven Goran Eriksson and he swiftly suggested Mark Hughes to owner Thaksin Shinawatra.
Hughes was named as City's new manager on Wednesday and the former Wales tactician immediately acknowledged the pressure would be on from the off.
"It is possible to break into the top four," he said. "I would be very worried if anyone in the football club started to think it was not.
"We are at a point in time where there are four very strong clubs in English football. But we had a point in time when they thought the four-minute mile could not be broken.
"What we have to do is develop an investment plan and a strategy to change that."
Former England boss Eriksson had built up a strong rapport with fans during his one year at the helm and Cook has acknowledged bridges need to be rebuilt in order for City to move forward.
"There are bridges that need to be built and we have to put some plans together about how you do that," he continued.
"It is not for me to comment about what happened before I or Mark arrived but it made people uncertain and uncertainty makes people think something is wrong.
"We are moving forward and I want the fans to come with us. After this week, once they see what we have got planned for them, I think they will."