Pierre-Emerick Aubameyang put Arsenal in front after just eight minutes. Nicolas Pepe collected a wayward corner kick on the right flank, then whipped in a cross that Vicente Guaita was able to get a hand to, but could only deflect into the path of the onrushing Aubameyang, who smashed home from close range.
"The main thing was to avoid a loss," Lacazette told Sky Sports. "We wanted to win, we started well but then we stopped playing. I think this is something we have to work on in the future.
"We showed we have character. Even when we are down we don't give up."
The visitors levelled soon after half-time when sloppy play in the back from Arsenal allowed Christian Benteke to collect the ball, charge into the area and fire a low shot past Aaron Ramsdale to make it 1-1.
Arsenal had chances after conceding the equaliser, but were soon behind when Odsonne Edouard blasted a shot into the roof of the net past Ramsdale from a rapid-fire Crystal Palace counter-attack.
Palace seemed home and dry after Arsenal left back Kieran Tierney blasted a shot from a tight angle into the woodwork but were punished for some sloppy defending deep into stoppage time.
A long throw-in produced a corner for Arsenal and after Palace failed to clear it and an ensuing goal-mouth scramble, Lacazette kept his wits and drilled in the equaliser past Guaita from close range.
Vieira, who won three league titles and four FA cups with Arsenal as a player, said Palace needed to stop conceding late goals in order to turn draws into wins.
"It was so close but we have been saying that a little bit too often," he told Sky Sports. "We have to learn from the games we played previously. I am really disappointed because the way the team came back in the second half, they deserved to win.
"I am frustrated for them, they were brave and showed character. We have to put our sleeves up and put our bodies on the line. We were really unlucky today, it is the way it is but I believe there is more to come.
"The players were really frustrated because we threw away two points. To concede a goal like that is really difficult to accept but these games will make us stronger."
Palace midfielder Conor Gallagher was thoroughly disappointed.
"Honestly, it's so horrible," he said. "It feels worse than a defeat, if that's possible. Nothing is worse than thinking that you've got the three points and have it taken away from you."
The result stretched Arsenal's unbeaten league run to five games and left them 12th in the standings on 11 points from eight games while Palace are 14th three points behind them.