The Canadiens, who host the Lightning at Bell Centre on Tuesday (7:30 p.m. ET; TSN2, RDS, SUN, NHL.TV), are 5-1-1 in the past seven games but the regulation loss came against the Blue Jackets on Tuesday.
It appeared to be a crushing blow to the Candiens' hopes, but they responded with the win over the Jets, who are battling the Nashville Predators for first place in the Central Division.
"Ups and downs of the season," Weber said. "Obviously that one hurt a little more against Columbus, but we know there was nothing we could do at this point except win our games. We just have to take care of our business. One game at a time.
"We won the first one we set out to win this week. Obviously, we had to do that to win all four. We have a lot of work ahead of us and we've got a good team [to play] on Tuesday so we'll enjoy it for a few minutes and then go home and get ready for Tampa."
Forward Jordan Weal, who had a goal and an assist against the Jets playing on the top line with Jonathan Drouin and Joel Armia, said the schedule in the week ahead suits him just fine.
"We've got three games here against good teams and that's who you want to play, play the best teams to get in because then you'll know we deserve it," said Weal, who was acquired from the Arizona Coyotes for forward Michael Chaput on Feb. 25.
"It was good to get this one back and stay in the hunt."
Weal has eight points (three goals, five assists) in 13 games for Montreal since the trade. He said that despite the tough road they have faced, the Canadiens' outlook has not wavered over the final weeks of the regular season and that outshooting the Jets 44-24 and earning the road win in Winnipeg proved it.
"Just shows the work ethic of the group in here," he said. "The day I came in here, you could tell it was a group of guys that really likes to be around each other and work for each other. That's really important to be a winning team.
"You've just got to keep pushing and keep pushing and not worry about the outside noise. It's tough. You're going to look at scoreboards. It's everywhere. You're scrolling through your phone and it pops up in your face. You just have to keep pushing."