With games against Arsenal and leaders Manchester City coming up, Hodgson stressed the importance of keeping up with teams immediately above them.
"We are closer to the pack and that's the important thing," Hodgson told a news conference on Thursday. "There is going to be a pack of teams for a period of time going forward in and around that third spot.
"Now we have ourselves within three-four points of that pack, it's important we stay with them. We can only hope to continue with what we've achieved so far. We aren't the finished article."
Palace's last-gasp 2-1 victory over Watford lifted them off of bottom of the table for only the second time since Hodgson took charge of the club.
They were also helped by the fact that relegation-threatened West Ham United and Swansea City failed to win in midweek.
"I don't think it's right to talk up or talk down the teams around you. We have enough pressure and responsibility. But if you ask am I pleased with what we have done in the last 10 games, the table does look better."
Mamadou Sakho is out of the Leicester game with a muscle injury while fellow defender Timothy Fosu-Mensah will have a scan after picking up a hamstring injury on Tuesday. Centre back Joel Ward is also out with a groin injury.
Leicester are eighth in the table with 26 points after seven wins, five draws and five defeats and are on a four-game winning run in the league.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Christian Radnedge)
