In a letter to Tessa Jowell obtained by the BBC, Pugh outlines concerns from a lottery body and a group working with voluntary organisations, who warn that a loss of funding would see a number of projects "go to the wall"
He said: "The fall in income will have a significant impact on the ability of distributors in Wales to meet their requirements and to fund worthy projects across the good causes.
"Any increase in the National Lottery’s commitment to the 2012 Olympic Games and the Paralympic Games will inevitably impact on Welsh distributors and Welsh good causes."
Pugh went on to add that the letter was just sending an early word of caution about who actually would be picking up the tab for the cost overruns. "If all cost overruns fell on the lottery, that could have quite a significant impact on sporting, artistic and cultural projects across Wales and that would be quite disappointing to see that happening," he added.