Former Middlesbrough coach Cooper and assistant Craig Hignett were recently installed as Pools' new management team following relegation to npower League Two and the subsequent sacking of predecessor John Hughes.
Hodcroft warned relegation and the Football League's new Salary Cost Management scheme will restrict the amount of money all clubs can spend on players next season, but added Cooper and Hignett, currently on a charity climb of Kilimanjaro, will be strengthening the squad.
"Their task will not be easy as funding for new players will be restricted by the stark reality of our return to League Two after six years and, of course, Salary Cost Management in League Two means we can only spend 55 per cent of our turnover on player's wages," Hartlepool chairman Ken Hodcroft said in a statement on the club's official website.
"So income into the club from all sources is important (especially from advertising and season-ticket sales).
"At the time of writing we do not know what the 55 per cent is as income (committed and projected) for season 2013/14 is still not known.
"Once the figures are compiled the club will then need the agreement and approval of them from the Football League. Poor income (actual and projected) will mean less to spend for Colin."
Hodcroft added: "If the number is low there will be no point saying: 'Cooper does not have the support and backing of myself or the owners'.
"Colin will have that support, but if the Football League says no to a player or a loanee, then Colin will have to make do with what he has.
"However, he is currently looking to bring in some new faces and we will work hard to justify them within our predicted income stream to the Football League before August. There will be a more detailed statement from the club on League Two salary capping in the next few days."