Irish defender Alan Sheehan became Parkinson's fourth signing of the summer last Thursday as the City chief continues to put his plans in place for the forthcoming 2014/2015 campaign.
With City due back for pre-season training next week though, Parkinson knows that he needs to add more bodies to the group before the club's Sky Bet League 1 curtain-raiser against Coventry City on Saturday 9 August.
Parkinson admits that his squad almost certainly won't be complete once day one of pre-season training come around but he is confident everything will be in place when the big kick off takes place in August.
Parkinson said: "My job now is the same as it has been all summer really, and that is to make sure that we have a squad in place that is competitive enough to move us forward once the new season comes around.
"We have a lot of work still to do between now and 9 August to get our desired team and squad moulded into shape so that we can be competitive in the division again.
"We are short on numbers when you look through the ranks but we are not the only club in this situation and I've come back for pre-season training with less players in the past.
"I am not overly concerned at the moment - it is just a case of being patient and making the right decisions with the money we have available in the budget.
"We know the squad size is not enough at the moment so we've got to get a few more in."