Forest had to settle for a point after Craig Davies cancelled out Andy Reid's goal for the hosts but the returning Forest manager was otherwise pleased with every aspect of the day.
He said: "For a new manager to step in and get that kind of reaction is superb. The team were great, the fans were great but we just could not get the result that would have topped it off.
"We tried so hard to get it and the fact that we had 23 shots to their five says it all. Shots were raining in on their goal and I said to the players at the end If you give me that effort, application, full-backs getting forward and chances created I can't complain.
"We've trained this week but it's the first time I have seen them on a big pitch. There's a lot of work to do but the fans must be pleased with the response from the players - I'm delighted by it.
"Bolton are a good side, who should probably be top two, but I'm sure they would accept they got away with murder."
Bolton boss Dougie 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."