The Reds striker refused to shake the Frenchman's hand before their meeting at Old Trafford last season after Suarez had been found guilty of racially abusing Evra in their previous encounter that campaign, and subsequently received an eight-match ban from the FA.
However, the two shook hands before Sunday's meeting and Evra is happy with Suarez on what was a day about respect.
"The most important thing today was respect," said Evra. "It was a game between two big clubs.
"There was a big tragedy. People were talking about a handshake but the stories of the clubs is bigger than that. If I hadn't shaken Suarez's hand, I would not be respecting the stories of the clubs.
"In the end I am glad this time he shook my hand. More importantly, it was important to respect the families. It was not an easy day."
United host Tottenham Hotspur at home Saturday in the Premier League.