Kagisho Dikgacoi's late header secured a hard-fought 1-0 win over Birmingham, Palace's first victory at home since December, to move them to within two points of the top six. Freedman has overseen a remarkable upturn in Palace's fortunes since he took over almost 12 months ago - not least with their stunning run to the Carling Cup semi-finals.
But the Scot is mindful his young side might be growing up too quickly following two seasons of relegation scrapes, and he said: "Deep down the back of my mind tells me we've got a small chance. But the front of my mind is realistic and tells me we are still growing and we might be growing too quickly, in terms of being contenders, but we'll give it a go."
He added: "I've got to be realistic with the lads and tell them to be patient and hopefully one day we will get there."
Dikgacoi's first goal of the season arrived with six minutes remaining as the Eagles finally found a way past Bo Myhill in the Birmingham goal.
Myhill made two fine saves from Mile Jedinak, while the woodwork denied Eagles skipper Paddy McCarthy, but Palace would not give up and the man known as 'KG' conjured up a dramatic late winner with a powerful header from Darren Ambrose's centre.
"It was a fantastic header and Darren put in a fantastic cross," added Freedman. "Everyone understands the game plan, we've no big stars, no heroes, we win and lose together and tonight underlined that.
"We kept on plugging away, we refused to let one in our net and we had the desire to put one in Birmingham's net."
Chris Hughton's side had their chances, with Curtis Davies scooping over the top and Stephen Caldwell heading too high.
"They are always tight affairs down here, they don't give much away," said Hughton. "But in the last 20 minutes I still thought we would get a draw at least. It could have gone either way."