Kelly left Rugby Park to join Bristol City last week and Nelson is now discussing a reported £50,000 transfer to League Two side Bradford. Shiels is disappointed to be losing Nelson, who joined Kilmarnock 12 months ago, but acknowledged the club have little choice but to accept an offer.
"Kilmarnock have accepted a bid from Bradford and I assume Michael will be a City player soon enough," said Shiels.
"Michael will be a massive loss for Kilmarnock. If you look at 2012 then Kelly and Nelson were two of our best players. They were integral and a huge part of the success story of Kilmarnock in 2012.
"It is important that we look after the finances of the club as they were not players that I wanted to lose.
"We can't look a gift horse in the mouth and we have to look to the future. The money that we have got in for Liam and Michael is not a lot.
"Kilmarnock are a club that is massively in debt in Scottish terms. The debt we are in supersedes the size of the club and I'm really sad to lose both of those players."