The Trotters appeared to have done enough to earn a replay against Premier League opposition as the clock ticked down at the Reebok Stadium with the two sides locked together at 1-1.
There was, however, to be a late twist in the tale as Johnny Heitinga snatched a stoppage-time winner for the visitors.
Freedman is disappointed to have seen Bolton's involvement in cup competition come to an end for another year, but believes his side are heading in the right direction.
On a game which was played in freezing conditions and with snow on the side of the pitch, the Scot joked: "We could have called the game off and left it for a Tuesday night, but we worked very hard to get the game on and it kicked us in the teeth, really. Disappointed, yes, at the result but not the performance.
"I felt that the first 20 minutes we started nervously and I can't quite put my finger on why we did and they deserved to go in front, but I felt that for the next 60 minutes we played as well as we have done since I have been here.
"We got a deserved goal and then tried for that winner, pushed everyone forward. A small detail at the end let us down. If you don't concentrate for 95 minutes against a Premier League side, they are going to punish you.
"There are lots of positives - Stuart Holden came on, Chung (Yong-Lee) played well, we had a good shape to the team, we passed the ball very well and created opportunities.
"It's very pleasing to see that and you can see there is light there. This club is going through a dip at this moment but we are all working very hard and you can see glimmers of hope there."
Freedman reserved special praise for Holden, with the American midfielder making a welcome return to competitive action at the Reebok following a wretched run of injuries.
He added: "He's worked very, very hard and continues to work hard. He got a standing ovation when he came on the pitch. He has got a long way to go, but he is certainly on the right path."