The Eagles spent under £7million in the summer on transfers, with the club only splashing out on James McCarthy, Jordan Ayew and Victor Camarasa.
Palace's transfer policy has come under criticism in recent years, despite the club currently enjoying its longest-ever spell in the English top flight, having been in the Premier League since 2013.
Hodgson manager admitted Palace need to get some players in in the upcoming transfer window.
When asked whether signing a contract to stay on until the end of the 2020-21 season would help recruitment, the 72-year-old said: "I would like to think that.
"Certainly what we have done over the last two and a half seasons with a group of players, many of whom were there right at the start in terms of my tenure at the club.
"A lot of work has gone in from these guys. They understand what we are looking for. They know how we work and how we work as a team, and these are the factors which are sometimes degraded in people's eyes.
"They think it's just a case of shipping people out and shipping new ones in. It's not quite as simple as that. I think we have formed a base.
"We have areas still, pockets where we need to improve and strengthen and everyone's on the same page where those pockets and areas are, and of course it's trying to find the players who fit that bill – and that's a lot harder.
"We know that's not a question of money alone. It's nothing so simple as that's a war chest, out you go and spend it. It doesn't always work that way.
"But the owners of the club are aware that we do need to get some players in and to do that will require some money."
Hodgson was appointed Palace manager in September 2017 and led the Eagles out of the relegation zone, with the club eventually finishing 11th, before a 12th-placed finish last season.
On the current challenges facing the club, he added: "We'll be working very hard between now and the end of the season to make sure that we stay in the league, because that is absolutely the be all and end all and our work in the next 10 games will be focused on that.
"But there'll be a side focus on checking out, scouting who we think are the right people, and that will mean the right price for the club and the right fit. And that's something every manager would say is an important factor."