Albion twice led only for Matty Cash to earn Forest a point at the death before Bilic's side were denied a winner to offside with virtually the last kick.
But head coach Bilic believes his team, who extended their lead to seven points for two and a half hours, are on track to return to the Premier League.
"I told the guys I'm going to be disappointed and they're frustrated, but if we continue like this, with the same patterns, focus, energy and quality, then we really have a good chance to do what we want to do," said Bilic.
"This was our best performance, whatever the result – we were always the ones who were better, in ball possession, in number of great situations, creating chances, everything was there.
"The only thing that was missing was to kill the game at 2-1. But some of our finishing was not good enough, and the goalkeeper made a few good saves."
"Yes it does, definitely. This was our top performance – we played excellently, considering the strength of the opponent and it was a derby game," he added.
Bilic felt Albion should have been allowed the winner at the end when Robinson volleyed home with Kyle Bartley lying on the line, only for the effort to be ruled out for offside.
"At the end, it was a goal. Callum Robinson was definitely onside but the only thing they may say is Kyle Bartley was influencing the game," said the Albion boss.
"Kyle was lying in the goal, so I don't see that as interfering in the game."
Bilic admitted Albion's second goal should not have been allowed but said he did not see Livermore's first-half foul on Yuri Ribeiro, which Forest head coach Sabri Lamouchi thought was a red-card offence.
The Croatian felt Cash could have seen red for a challenge on Filip Krovinovic after he had already been booked.
"Our second goal, yes it was a foul for them, on Ameobi," he said.
"It was a very difficult game for the referee, like the derbies are. It was a very pacy game.
"There were a few things. I don't blame the referee but I can explain them.
"The first controversial one for me was Matty Cash challenge on Filip Krovinovic. Today that's a yellow card and he was already booked.
"He got the ball so we can talk about great tackles, but nowadays we've been told from seminars that that was a reckless challenge, 100 mph. So for me he should be off."
Lamouchi hinted that the second goal should not have been allowed.
"Some people and refs can make mistakes," he said. "I made mistakes on Tuesday maybe and will before the end of the season and we must help them of course. But decisions can change the game.
"I have a lot to complain about. But I am the manager of Forest and must be positive with people, it's part of the game."
Lamouchi also claimed VAR should be extended to the Championship to help make decisions.
"We play football but not with the same rules as the Premier League. They play with VAR and without it you end this game with some tension," he added.
Robinson's first goal for Albion and Figueiredo's 65th-minute own goal saw the Baggies twice lead, sandwiching Forest's equaliser through Bartley's 45th-minute own goal before Cash earned a point.