Saints have made an encouraging start to the post-Keiron Cunningham era, following up their battling defeat with 12 men at Wigan Warriors on Good Friday with a 26-22 win over leaders Castleford Tigers at the Totally Wicked Stadium on Easter Monday.
Now bottom-placed Widnes stand in the way of their route back to the top four as clubs reach the halfway mark in the regular season.
"We were delighted with the outcome on Monday, especially after backing up a really tough Wigan game," said Traynor, St Helens Under-19s coach who is sharing responsibility for the first team with Sean Long and Jamahl Lolesi following the sacking of Cunningham.
"But we honestly believe we can improve on that and get better and the big thing is the lads believe that themselves.
"We have played two top teams - Cas have been running hot and Wigan is always a big game - and the last thing we need to do now is drop our intensity because of the position Widnes are in.
"We have to get our approach right as they are a dangerous team. We can't drop our standards and, if we maintain that, then hopefully we can come away with a win. We can't fall in love with ourselves because we have tried hard for two games and come up with two decent performances.
"Our philosophy is every time you pull a Saints shirt on you give your ultimate effort, so you aren't going to get praise for putting effort in. It's skill, intensity, brains and game sense we want to improve on."
Saints are still without experienced trio Jonny Lomax, James Roby and Ryan Morgan but are boosted by the availability of ever-present prop forward Kyle Amor, who was not suspended following his dismissal in the 29-18 defeat at Wigan after his charge was downgraded.
Widnes' injuries woes have continued with the loss of centre Tom Armstrong, hooker Lloyd White and half-back Danny Craven but assistant coach Mick Cassidy says the players still have the belief they can turn their season around after winning only one of their first 10 matches.
"We know we can score points," Cassidy said. "We are just lacking a bit of defence when the game gets tough."