Malky Mackay says he will not resign as Cardiff City manager despite owner Vincent Tan's criticism.
"I will not resign from my post," Mackay told BBC Radio Wales Sport.
And the 41-year-old Scot added that Lim's statement on Monday had surprised him.
In it, Lim said Tan felt Mackay had already been given sufficient funds to keep the club in the Premier League.
In the exclusive interview, to be broadcast on Tuesday on BBC Radio Wales, Mackay said he had heard nothing from Tan or Lim before Monday's statement.
"I was surprised obviously, but at the same time my job doesn't change," said Mackay, who guided Cardiff City to the top flight last season after a 51-year absence.
"It's a job only three-quarters done as far as I am concerned - making Cardiff a sustainable Premier League team.
"I have a great group of players who are competing at this level and enjoying this level. The fans are enjoying being at this level and my duty is to make sure we continue to do that.
"It would be wrong of me to walk away from a job because the owner doesn't want to give me money in January.
"I have been in situations before when a board has had no money."
In Monday's statement, Lim claimed Tan was "extremely upset" to read quotes from the manager concerning the possibility of new recruits and said that Mackay's comments had unfairly raised supporter expectations and placed unnecessary pressure on the club.
Mackay, whose side are 15th in the table, made his comments about future transfer dealings following Saturday's 1-0 win over West Brom.
"It would be great if we can bring in three quality additions to the squad," the Scot had said, adding he was after "a defender, a midfielder and an attacking player".
A Cardiff City fans group backed Mackay after Tan's public criticism.
"It's a very sad state of affairs," said Tim Hartley, chair of the Cardiff City Supporters Trust. "The fans will back Mackay because he is popular."
Hear the full interview with Cardiff City manager Malky Mackay on BBC Radio Wales Sport.