Pugh, in an interview with a local radio station, said he felt Cherries needed a few more players in order to be pushing for the play-offs again.
Asked which area of the squad he felt needed strengthening, Pugh replied: It's not really fair for me to say, that's down to the gaffer. I do think we need a striker who will score 15-20 goals a season. That's what we lacked last season. We sold two strikers and it is important we bring someone like that in.
Cherries have so far added four players to their squad this summer goalkeeper Darryl Flahavan, defender Adam Barrett, midfielder Steven Gregory and loan signing Scott Malone. Jason Pearce, Rhoys Wiggins and Danny Hollands have all left the club.
Mitchell, in response to Pugh's comments, said: We do need a 15 to 20-goal striker but, hopefully, we have got at least one already. I think Danny Ings, Michael Symes and Steve Lovell are all capable of scoring 15 to 20 goals if they play consistently.
We would all love someone who is guaranteed to do that and I am sure every club would say the same.
As regards more players, of course we need more. We need players to push the ones we have got.
But we have got 26 and I don't think we want to go too mad otherwise we would run over budget and we are not prepared to let that happen.
We have just signed a left-back on loan and are still looking for a right-back. I think Lee has the makings of a good team this season.
In his interview, Pugh also said he was sure the club's management team was working hard behind the scenes to bring in players, adding that he was sure it will all come together.