Having knocked out Nottingham Forest and Liverpool before securing a last-gasp draw with Everton, the Latics' memorable cup run came to an end on Tuesday night as they lost 3-1 in the fifth round replay at Goodison Park.
But with only one point between Oldham and the relegation zone Furman knows they need to repeat their cup displays on a regular basis in the final 13 matches of the league campaign.
"We have to take the confidence out of what has been a terrific cup run for us and we've got an important 14 or so games left in the rest of the season now," he said.
"It's vital that we take some of the form that we showed over the past few weeks and in patches on Tuesday into the remainder of the season."
The hard-working display the Latics put in was certainly appreciated by the home support who applauded the Oldham side off the pitch at the final whistle.
"It was great, the appreciation they showed us," Furman said. "The atmosphere was brilliant.
"Our fans were great, their fans were great and to get an ovation from their fans coming off the pitch was a special moment for us and it shows that they (Everton fans) appreciated how hard we worked."