Fulham breathed new life into their battle to stay in the Premier League with a hard-earned victory over Aston Villa last Sunday.
Hodgson, though, knows that will count for little should the Cottagers fail to build on their performance when they travel to Middlesbrough this weekend.
“I get the feeling the more we work together, the better they know me and the better we play – hopefully that will be good enough to keep us up,” said Hodgson, who took over from axed Lawrie Sanchez in late December.
“I feel more comfortable all the time, and am hoping over the next 13 games things will be on something more of an even plane.
“It is up to us to show we are good enough to stay in this league.”
Hodgson insisted: “However, the moment we start believing that because we have got a result somewhere, it means things are going to change and will become much easier, that would be a very foolish step.
“We have to accept that every game is a real test and a challenge – unless we can reproduce 13 times what we did against Aston Villa then we can get beat and will be divorced again – what advantage we have in being brought closer to the mix will be lost.”
Fulham have had 12 senior players away on international duty this week and Hodgson admits he expects “some will be tired” on their return to west London.
However, Hameur Bouazza has been granted special leave to deal with a family matter after his mother was taken ill.
American striker Brian McBride is, though, in contention to start following his return to fitness after a serious knee injury suffered against Boro at Craven Cottage back in August.
