Luka Milivojevic scored the game’s opening goal from the penalty spot after Federico Fernandez brought down Ruben Loftus-Cheek inside the area.
Jordan Ayew equalised for the home side with 15 minutes to go, firing in from the edge of the box after he squeezed past Milivojevic.
When asked about the result, Hodgson said: “A draw probably fair. They had more possession, they move the ball well, but we controlled that and didn't concede too many chances.” He added. “We looked dangerous in attack.
“We've been bottom for a large part of the season so far, but we're picking up points. Being offered four points from Leicester and Swansea away, I'd be satisfied with that.
“We've brought ourselves up into a pack of teams,” the 70-year-old said, “who will now be looking over their shoulders at the spectre of relegation. We've caught them up before schedule, but there's an awful long way to go. A scrap for every point.”
“Swansea scored an excellent goal”
On the goal that Palace conceded, Hodgson said: “Swansea scored an excellent goal, really good piece of football, the last 15 minutes became end-to-end.”
Ayew’s strike was actually the first goal he has scored since the 2-0 away win against Palace in August.
After extending their unbeaten run to eight games, Hodgson said: “From our point of few, we’ve been down there at the bottom but we’re picking up points now, We have to be satisfied because we can’t be thinking we turn up and beat everyone."
After picking up four points from two away trips to Swansea and Leicester City, Hodgson said: “We can be more than satisfied with the return we’ve had in the last two games.”
On Leon Britton’s sudden appointment, Hodgson said: “I’ve no idea what he’s been able to do in few days. Journalists will always be believers in the magic wand, you believe all the problems disappear. It’s taken me three and a half months working every day to get a team I can identify.”
The Eagles currently sit 16th in the table, two points clear of safety and next up for Palace is a home fixture against Arsenal on Thursday.