Wanderers looked set to be heading for a replay after Marvin Sordell cancelled out Steven Pienaar's early goal, only for Johnny Heitinga to break home hearts with a late winner.
Freedman said: "I am disappointed in the result but not in the performance. We started nervously and they went a goal up, but I felt we handled it and it didn't set us back.
"For the next hour we played possibly the best football since I've been here. We got a deserved goal and pushed everything forward for a winner, then a small detail let us down at the end.
"We are going through a difficult stage at this club but it is very pleasing for the fans to see that we are all working very hard and you can see some glimmers of hope there."
Freedman reserved special praise for Stuart Holden, who came on as a late substitute to make his first appearance at the Reebok Stadium since March 2011 after a serious knee injury.
Freedman said: "It's very emotional for everyone because Stuart has worked very hard. He has got a long way to go and will be playing in the reserves on Monday night. He is certainly on the right path."