The black, green and gold ended a troubled 2020 on a high as they bagged a bonus-point success against Worcester Warriors on Boxing Day.
And with their 12-match losing streak now put to bed, Saints are desperate to kick on.
They face a big derby date with Leicester Tigers on Saturday, January 9.
And after a couple of Champions Cup matches, Saints then close out January with a trip to Gloucester.
And Haywood, who came off the bench to score the bonus-point try against Worcester, said: "We've got Leicester and then Gloucester so it's going to be a big month for us.
"We can get the momentum on an upward curve or we can go back down so the boys are ready for the challenge.
"We want to back up what we did against Worcester with a win against Leicester."
Haywood saw Saints struggle to back up their top four finish as they finished eighth in the previous Premiership campaign.
And he said: "I wouldn't say we were lucky to get top four that season but it was the lower end of the points total you normally need.
"We had some lads coming in who were performing well for the Wandies and they were then putting the performances in for the first team to secure their positions.
"The hard thing then is to back it up again, which we obviously didn't do, but hopefully we're getting back in the position where the boys are going to start being confident with what they're doing.
"It's about winning at the end of the day. You can talk about performances but you're scrutinised on whether you win or lose."
Saints struggled at the end of last season and at the start of the current one.
"It kind of backed on to the end of last season because we went with a split team approach and it didn't really work," Haywood added.
"There were games in that we probably would have won if we put out our best sides for the games but it was a tricky time.
"If you come to the end of the season and you've got nothing left it's a tough one.
"It's not been frustrating for me because I've seen the boys putting in the effort off the pitch and all the hard work we've been doing, hopefully we can get the rewards.
"The Worcester win is still only one win and we want to back it up so hopefully we can do that against Leicester."
Haywood's presence on the pitch is always a big boost for Saints.
And he has been doing as much work as he can behind the scenes to get in the best possible shape to perform after a knee problem.
"A couple of years ago I tore my ACL and MCL and during the lockdown time I got a bit stiff and scar tissue built up so I had a clean-out," he explained.
"It was just general getting back moving, getting strength back into it, getting running again and then getting playing again.
"It feels much better now and I can actually walk up and down the stairs without it hurting.
"I would say at the back end of last year I felt the wear and tear but I don't know if that's because I put on a bit of weight after my ACL and MCL injury.
"I wanted to put extra weight on so that I was slightly bigger and stronger for the scrum, but it didn't really help me.
"I felt slow and sluggish and couldn't do stuff I would normally do, so over the past 12 weeks I've dropped a bit of weight and I'm feeling fitter and can move better.
"I'm a bit more agile so hopefully I can have a bit more of an impact on a game.
"Now I'm trying to play my game again, get my hands on the ball a bit more and find myself in the wider channels because I'm a good passer and I can be effective putting a winger in at the corner."