The Eagles are 18th in the Premier League table after a disastrous start to the campaign under former boss Frank de Boer.
Palace replaced the Dutchman with Hodgson although it took the former England manager a few weeks to settle down at Selhurst Park.
He concedes his team are now playing catch up this season, but they are unbeaten in their last four matches and starting to climb the table.
With the transfer window open in a month's time, Hodgson is eager to add more bodies to his squad as he tries to steer his team away from the drop zone.
He told Sky Sports: "If we'd have got the same number of points (10) from the first seven games, we'd have been middle of the table which at the moment would be an area we'd be more than comfortable to be in.
"But we are playing catch up. We have shot ourselves in the foot.
"The more money they can give me to spend the happier I shall be because you would hope the more money you have, the better the quality the player you'll have. But that's not an exact science.
"If ever you want a science where risk is at the highest possible level it's spending money on transfers to buy football players and pay them wages and hoping that you're going to see scientifically that you got value for your money."