Forest had to settle for a point after Craig Davies cancelled out Andy Reid's goal to deny returning boss Billy Davies an opening win at the City Ground.
But with the hosts having 23 shots compared with Bolton's five, it was a hard-earned point for the visitors, who also had Marcos Alonso sent off for two yellow-card offences.
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 (Adam Bogdan) 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."