Palace and Leeds could not be separated at Selhurst Park as United's return to Premier League action after a 15-day break ended in a goalless draw.
Vieira, though, felt his side had more than enough good moments in which to win a feisty game which featured plenty of challenges and decisions, one of which left the Palace boss miffed in the first half.
Palace forward Wilfried Zaha was involved in much of the night's drama and the Ivory Coast international caught Whites winger Raphinha with an outstretched hand midway through the first half.
Raphinha hit the deck and was eventually awarded a free-kick but Vieira played down his conversation with the fourth official about the incident in his post-match press conference and also applauded the actions of Zaha throughout.
"I think the referee was in a position where he didn't make the decision," said Vieira, asked what his first-half conversation with the fourth official was all about after the Raphinha and Zaha incident.
"The fourth referee (official) made that decision and this is what they are for, to help the referee to try to make the right decision and he thought that was a foul and I thought it wasn't a foul so nothing big in there."
Asked about Zaha being involved in various scraps and confrontation and how he think he handled the physicality of Leeds, Vieira said: "I wasn't worried at all.
"I think he is used to it, I don't think this is the first time and I don't think it will be the last one.
"I think he showed a lot of maturity and tried to concentrate on the game and play and that's it."
Palace served up 17 attempts at goal in Monday night's contest, seven of which were on target but Whites 'keeper Illan Meslier was not for passing.
Leeds managed nine attempts at goal but just two on target and Vieira felt his side would have been worthy winners.
"I don't know, I think you can put that down to our decision making, trying to find maybe a team mate in a better position," said the Palace boss.
"I think we were unlucky at times as well but I think we created enough situations or chances to score and we didn't.
"I think it's just about taking our chances and we have quality, we know that the front three can score goals.
"But, yes, I would want them to score more regarding the number of chances that we are creating and today I think we were unlucky.
"I think the only thing that was missing in our game was that goal.
"When you look at their (Leeds') front four, they play with a lot of intensity and try to close people down and I was really happy because we moved the ball well, we moved it quick enough to create those kind of overloads on the side and we had a couple of good crosses.
"I think our tempo of our passing was good."