The Eagles looked set to claim bragging rights over their rivals thanks to Wilfried Zaha’s first-half penalty but Neal Maupay levelled for the visitors in the 95th minute to earn a share of the spoils at Selhurst Park.
It means the south Londoners have still only tasted victory once since Vieira replaced Roy Hodgson in the summer but aside from that important statistic the other signs are positive.
New additions Marc Guehi, Joachim Andersen and Conor Gallagher have quickly become integral while the style of play has been transformed almost overnight from the rigidness of the old regime to a dynamic possession-based team who press frantically from the front.
“You can see the new players are all settling well, they are playing well and the team is improving,” captain Milivojevic said.
“Me as a team-mate, I am so happy for them and I am here to help them to adapt as quick as possible but with their quality, they’ve already adapted properly.”
The draw leaves Palace on six points after six games but they could have claimed all three on Monday with Jordan Ayew firing wide when put through on goal with 13 minutes left.
It left the door open for Brighton to grab a dramatic equaliser with Vicente Guaita’s poor kick returned before Guehi could not clear Joel Veltman’s pass which allowed Maupay to run off Cheikhou Kouyate and lob in to spark wild celebrations in the away end.
Milivojevic added: “We deserved the three points. We were a bit naive but that’s okay, we have the next game (against Leicester) and we have to continue.
“We’ve been dominant for most of the game but we had chances to score the second and finish the game. When you don’t convert your chances, you can be punished.
“We put a lot of pressure on them, took the ball high up the pitch which is something we want to do but we should be more clinical.”
Eagles manager Vieira described the late goal as “brutal” and he conceded the confidence of Ayew needs to be repaired with the Ghana attacker now without a goal for Palace in 35 games, a run dating back to November.
“Jordan in the dressing room was like every other player, everybody was really disappointed not to take those three points,” the 45-year-old said.
“Obviously Jordan missing that chance was important but when he doesn’t score, especially as a forward, there is a lack of confidence and self-belief in your ability to score.
“It is my responsibility, with my staff, to bring him back to what we know he can do and that is scoring goals. We just have to find his confidence back and he can score goals, there is no doubt about it.”
After Maupay grabbed his fourth effort of the season, the French forward cupped his ears to the Palace fans in a similar fashion to how Zaha had done to the travelling faithful earlier in the game.
“Football is nothing without fans and some involvement with players,” Brighton’s hero told Sky Sports.
“The atmosphere was really tough and when I scored I looked at Zaha and smiled at him because when he scored his penalty he celebrated and he gave some to our fans.
“I won’t say what he said and what I said but you know how it is on the pitch with players sometimes. You give banter on the pitch sometimes and it was the perfect time to give him something.”
Palace and Brighton have been asked by the Football Association for their observations of the ugly scenes at full time, the PA news agency understands.
James McArthur and Seagulls goalkeeper Robert Sanchez clashed and were booked by referee Andre Marriner soon after he brought the match to an end.
Away captain Lewis Dunk, who had celebrated the late leveller in front of Palace supporters, then received a volley of abuse from fans as he left the pitch which saw the two sets of players come together again near where the dressing rooms are located.