The Eagles were handed a stoppage time penalty after a foul on Wilfried Zaha, but the Belgian's tame effort was comfortably saved by Asmir Begovic, who rescued a 2-2 draw for his side leaving Palace bottom of the table.
Benteke's miss proved costly for the south Londoners as Swansea City and West Ham United, the two sides directly above them, both won. Hodgson was also left fuming by his striker's decision to take the penalty after he wrestled the ball off Luka Milivojevic, Palace's designed penalty taker, who had already converted from 12 yards earlier in the game.
"If we get relegated and two points in May would have kept us up, I'll say maybe these points are the ones that cost us," the former England manager was quoted as saying by the Telegraph.
Asked whether Benteke will feel guilty about his miss, Hodgson replied: "I'm certain he will.
"Knowing him not terribly well, he will be the sort of guy who will be thinking that way – 'I need to make this up, I didn't score that penalty that I really wanted to take so I owe you one'. Who knows. Maybe we will win a game by the odd goal and it will be some piece of magic from him and all this will be forgotten."
Benteke, who became Palace's record signing when he joined from Liverpool in August 2016 for £32m, is still to find the net in the Premier League this term and his lack of form has taken a heavy toll on Palace, who have the league's second-worst offensive record.
However, Hodgson dismissed the idea that Benteke opted to take the penalty himself to break his goalscoring drought.
"You cannot use that as an excuse," Hodgson added.
"The fact is a lot of other players would like to get off the mark. James Tomkins would like to get off the mark for the season. The goalkeeper would like to score a goal. You cannot use that one."
Since 70-year-old Hodgson replaced Frank de Boer in the dugout at Selhurst Park in September, the Eagles have picked up 11 points in 12 games, after losing their opening four matches without scoring a goal.
However, Palace remain two points adrift of safety and face a potential season-defining run of games, with trips to Leicester City and Swansea sandwiched in between home fixtures against Watford on Tuesday night, Arsenal and Manchester City.
Hodgson, however, insisted there was no reason to panic yet.
"We've been bottom for 15 out of 16 games," he said in his press conference on Monday.
"We started the season with 0 points, 0 goals and 19 against. The fact we're still bottom isn't a major surprise, but we will get on with the job and do what we need to do."