The Tykes headed to The Hawthorns sitting bottom of the Championship but stunned the home crowd with a brace from Cauley Woodrow putting them in a commanding position.
But they fought back after the interval with a Bambo Diaby own-goal and a Matheus Pereira header earning the Baggies a point.
"Considering everything that happened in the game, especially in the first-half, we have to take this point," Bilic said.
"It is a fantastic point for us.
"We started okay but after 10 minutes we started to rush things.
"We were trying to play key balls, assists almost, when it wasn't the situation to play them.
"We were rushing things. And then we made it worse - we conceded two goals.
"They scored one, then they scored a screamer and all of sudden it becomes very difficult.
"The team talk at half-time was a calm one. We wanted the guys not to rush things.
"The key point was that we couldn't concede a third because then it is game over.
"I was quite confident we would put them under pressure, that we would create chances.
"We showed not only character and spirit - but maturity that we can stay in a game.
"I will never settle for a point - home or away - but considering everything we have to congratulate the players because it is a fantastic point."
Pereira's goal came from a wonderful cross from substitute Conor Townsend who replaced Nathan Ferguson at half-time.
Ferguson, primarily a right-back, has impressed at left-back for the past few months.
But Bilic felt his team needed a natural left-footer on that side and in the end that change helped inspire Albion's comeback.
"Nathan wasn't injured," the head coach continued.
"We had to take some risks. It was a tactical change because we wanted to come into those pockets and then wide.
"It was very difficult to break them through the middle - they had five defenders plus two midfielders.
"We wanted to go wide and half-wide.
"But we needed a left-footer on the left side - with Conor pushing up high. It was a tactical change."
Matt Phillips missed the clash against Barnsley with a shin problem - the same issue that kept him out of Saturday's win at Middlesbrough.
“I was expecting him to be available tonight, to be fair,” Bilic added.
“Unfortunately, he wasn’t.
“He’s had a scan yesterday, and I’m expecting him to be okay for Saturday. He should be. You never know.”
Meanwhile, Albion technical director Luke Dowling has moved to assure fans the club remains optimistic Ferguson will commit his long-term future to the club.
The 19-year-old, who is out of contract in the summer, burst on the scene at the start of the season after impressing Bilic in training.
But his performances have led to interest from elsewhere with Tottenham, Crystal Palace, Juventus and Atletico Madrid all believed to be monitoring the teenager.
“I wanted to assure you that we remain in positive dialogue with Nathan’s advisor and, most importantly, his parents who are wonderful people,” Dowling said.
“We should all remember what a tumultuous few months Nathan has experienced at such a young age.
“From turning up for pre-season training perhaps hoping for some sessions with the first-team and maybe a loan somewhere, he finds himself starting at Nottingham Forest, scoring his first goal and playing an impressive role in our start to the season.
“We obviously feel that this is the best place for Nathan to continue his exciting development and I remain optimistic we shall be able to agree a new contract with him in time.”