The defender felt respect was the key word in difficult circumstances on Merseyside as tributes were paid to the 96 fans who tragically lost their lives at Hillsborough.
"It's unbelievable," he enthused to MUTV. "To be fair, I always say one of the best sensations is when we win at Anfield.
"We've been coming here for four years [almost five years], a long time and I've not been seeing a dressing room like that with smiles on the faces after the game. I want to win against Liverpool. If I play badly or play well, I just want to win and that is what we did."
Evra shrugged off the pre-match talk about his handshake with Luis Suarez to instead focus on the bigger picture.
"It was not an easy game," he stressed. "There was a lot of tension and emotion beforehand and, in the end, we get the three points. It's all we talk about - winning - because we have done our job and well done to everyone.
"I think the most important word today was respect because it was a game between two big clubs that have both had big tragedies. That's why, although a lot of people were talking about me shaking hands with Suarez, the story of the clubs is bigger than that. It's why I think if I didn't shake his hand, I didn't respect the story of both clubs.
"In the end, this time, he shook my hand and it was more important to respect the families who lost a lot of people."