Indeed, the frustration deepens for the Canadiens, who are 0-5-1 in their past six games and sit six points behind the Florida Panthers for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
Montreal next plays at the Detroit Red Wings on Tuesday (7:30 p.m. ET; FS-D, TSN2, RDS, NHL.TV).
Kovalchuk has been a popular topic in Montreal since signing a one-year, two-way contract last Friday worth $700,000 at the NHL level and $70,000 if he's assigned to Laval of the American Hockey League.
The move came after he was a healthy scratch in his final 18 games with the Kings before he was placed on unconditional waivers Dec. 18 and had his contract terminated.
As a result, the 36-year-old forward, who is in his 13th NHL season, has been described as a low-risk acquisition. The Canadiens are hoping he'll provide some offensive punch, especially on the power play, on a roster that's depleted by injury; four of the team's top nine forwards -- Brendan Gallagher, Jonathan Drouin, Paul Byron and Joel Armia -- are currently on injured reserve.
On Monday, 2:28 of Kovalchuk's ice time was on the power play, second only to Max Domi. At even strength, he played on the team's top line with center Philip Danault and left wing Tomas Tatar.
There's some question as to where Kovalchuk will slot in once the injured players return, but that isn't a concern for now, not with the ailing Canadiens skidding badly.
"It's easy to play with good players, but we've still got a long way to go," Kovalchuk said. "Our power play, we tried to pass a little too much. We have to be more simple, shoot the puck. It's a learning process, it's going to take a little time, but coaches explained to me what they're looking for with their system. That's what I tried to do."
Kovalchuk's first game in a Canadiens jersey was the most highly anticipated debut of a Montreal player nicknamed "Kovy" since Alex Kovalev, who arrived in a trade with the New York Rangers on March 2, 2004. Kovalev would become a popular player with Canadiens fans over his five seasons, scoring 264 points (103 goals, 161 assists) in 314 games.
Kovalchuk, perhaps coincidentally the 17th Canadiens skater onto the ice for warmups on Monday, has good-naturedly bought the use of No. 17 here, the only sweater he'd worn for his 897 NHL games prior to his Montreal debut. It was the jersey number of late, legendary Hall of Fame forward Valeri Kharlamov, the favorite of Kovalchuk's father. Kharlamov first came to prominence in North America at the Montreal Forum on Sept. 2, 1972, scoring twice for the Soviet Union in a 7-3 victory in Game 1 to begin the historic eight-game Summit Series.