However, Parkin has insisted Notts are well prepared for the current campaign despite the lack of numbers.
"I do think there is a good squad here," Parkin told the Evening Post.
"There are talented players in the ranks and the new signings look good.
"But it would be nice for Billy to be able to bring in one or two more new faces.
"I think they are needed. We are close to getting there, but there are one or two areas that still need strengthening.
"The new players already look as though they are part of the side, but it would be nice to bring in one or two more."
Parkin then went on to say the trip to Italy was a huge success and helped the new signings settle in.
"It was a hugely valuable trip," Parkin added. "Things were just about perfect.
"The important thing is that the new players have had the chance to bed in and get to know the other lads. That has happened in a big way. Everyone has got on superbly."
With the Magpies playing their first friendly at Meadow Lane tonight, things are beginning to look more promising.