Craig Davies cancelled out Andy Reid's goal - the first of Billy Davies' second spell with the Reds - but Wanderers were on top when Alonso was booked for the second time.
Freedman said: "We had a game plan to be cautious at the start and build momentum in the second half but the sending off was difficult to take.
"We had to dig in deep but I thought we did that and deserved the point we got on a day that was always going to be a hard one.
"Our goalkeeper did well for us. It wasn't just his saves - that's what he's there for - but his organisation and willingness to come and take responsibility was important for us.
"We knew what to expect with a new manager coming in to Forest this week. Billy knows what he is doing and although expectations are high, there are a lot of clubs capable of getting into the play-offs and Forest are one of them."