Montreal lost the Cup Final to Tampa Bay in five games.
"I think if you ask anyone in the North Division who had to play [the Canadiens] nine or 10 times, they can tell you it's not surprising," McDavid said. "Their team was built for the playoffs, they're big and strong and mean and they've got four lines that just all roll over and do the same thing. They obviously have one of the best goalies (Carey Price), if not the best goalie, backing them up, so they're a real solid team, and we certainly had battles with them, and they had a great month."
The Oilers were 4-4-1 against the Canadiens this season.
Edmonton on Monday acquired defenseman Duncan Keith along with forward Tim Soderlund in a trade with the Chicago Blackhawks for defenseman Caleb Jones and a conditional pick in the 2022 NHL Draft.
Keith, who turns 38 on Friday, won the Stanley Cup with Chicago three times (2010, 2013, 2015) and was selected as one of the 100 Greatest NHL Players during the NHL Centennial season in 2017.
The Oilers have also re-signed forward Ryan Nugent-Hopkins to an eight-year contract worth $41 million (average annual value $5.125 million), and reportedly are in talks to re-sign goalie Mike Smith and extend defenseman Darnell Nurse.
McDavid was a unanimous selection for the Hart Trophy as MVP after the center scored 105 points (33 goals, 72 assists) in 56 games this season. Edmonton, which was swept by the Winnipeg Jets in the Stanley Cup First Round, has won one playoff series since he made his NHL debut in 2015-16.
"Well, I think you know when it first ends, you never really want it to end and it takes a little bit of time to get over that, and then, at a certain point in time to get ready to get back at it," McDavid said. "Certainly now that the season's over and the Cup's been handed out, the focus shifts to next year and everyone will be getting ready to go for a big year next year."
NHL.com staff writer Mike Zeisberger contributed to this report