Blaze head into the weekend holding a five-point advantage over ninth-placed Manchester Storm, with both teams having four regular season games left.
Storm have a double-header against Braehead Clan while Blaze – on a five-game winning streak – are in action just once with a trip to leaders Sheffield Steelers on Sunday.
Weber said: “The biggest thing for me during this five-game period is we have held Cardiff, Sheffield and Nottingham to four goals in three games.
“They are three very talented teams and against Cardiff and Nottingham we have kept them to mid-20s in shots. We are doing all the little things right.
“There have been flashes and snapshots throughout the year but we have seen some improvements and we are playing with a renewed sense of energy and our puck management is better.
“We are now focused on the first period in Sheffield on Sunday. We want to continue our run of playing the right way.”
Blaze have won their last six meetings with Steelers, but Weber knows his side must maintain their recent standards if they are to move a step closer to qualifying for the play-offs.
He added: “Sheffield are too talented not to create chances, but that is why we have Stewie (Brian Stewart) back there to help bail us out and he has been doing a fantastic job.
“When you go on a winning run against a team it gives you confidence and hope – and that is a strong drug. We know we can play with any one of the nine teams.
“But the guys are also aware if they don’t play the right way, don’t do the little things and don’t outwork the opposition we will get beat. It is such a fine line.”
Coventry’s recent good form was recognised on Thursday when forward Brett Robinson was named the Elite League Player of the Week.
Robinson scored three goals and added a further six assists as Blaze won all three games they played.
He said: “I had a slow start and I was frustrated, but things have been picking up lately it is maybe not a coincidence that we are starting to win as well.
“I have to thank my line-mates Chris Bruton and Carl Lauzon – we have been clicking lately.
“It feels good not only for myself, but we are on a five-game winning streak and whenever you are winning like that it feels good.
“Other accomplishments are nice but it is more important to get the wins.”
(Image permission: Scott Wiggins)