Hodgson's first game in charge on Saturday ended in a 1-0 defeat by Southampton, condemning Palace to a fifth successive Premier League loss without scoring a goal.
Bakary Sako's 12th-minute header earned a 1-0 win against Huddersfield Town in the League Cup third round, with Palace having lost to the promoted side on the opening day of the season under Ronald de Boer who was sacked last week.
With league games against Manchester United, Manchester City and Chelsea looming, Palace could be in for more pain but Hodgson took some encouragement from Tuesday's win.
"I'm very pleased with the win and the first half performance, especially after a week's work," he said.
"We still have a lot of work to do tactically with the players until we are satisfied that we can produce the level of the first half performance for a longer period.
"However, it would be very churlish of me not to praise the players and I am very happy with the contribution tonight."
Hodgson has performed relegation-saving marvels at West Bromwich Albion and Fulham but Palace's plight represents a huge challenge for the 70-year-old former England manager.
"You don't repair the damage we've suffered overnight; it's going to be a long, hard process but I know that there's light at the end of the tunnel and saw some shards tonight," he said.
(Reporting by Martyn Herman; Editing by Ken Ferris)
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