Cardiff Blues face French giants Montpellier at BT Sport Cardiff Arms Park on Friday night (kick-off 7.30pm).
Six days later the teams will battle it out once again at the Altrad Stadium in the south of France with the two pool games going a long way to settling qualification hopes.
And Defence Coach Steadman, who joined Cardiff Blues in the summer, is hoping the defensive edge showcased in the win over Connacht will be repeated as the team hunt more European success.
“I have been encouraged by the last few weeks and the signs have been there all season,” said Steadman, a former Defence Coach with Scotland and Ireland.
“One or two individual errors have cost us against good teams, but what I touch on each week is consistency and the boys are showing that now.
“The Ospreys game away, in testing conditions, I was really pleased and then to back that up with five-day turnaround leading into Connacht was good.
“We know we have got to show more consistency going forward and that must happen on Friday against a very powerful team in Montpellier.
“The input of Gethin Jenkins and Sam Warburton, and what they have brought back from international duty with one or two of the other boys, has been invaluable,” he added.
“We’ve got some big fixtures over the next few weeks. Back to back with Montpellier and then the derby games over the festive season.
“It’s a massive month for us into the New Year. We’re in a good place, there is a good feeling here and that’s all set up by enjoying your victories.”
Former Great Britain, York Wasps, Featherstone Rovers and Castleford rugby league player Steadman admits he still wants more from his players despite the win over Connacht.
“Our technique was still poor against them. It was down on the TV as 26 missed tackles… but I counted 29.
“To get a result at any level of rugby is a massive effort and our scramble defence was quality. But we can’t afford to be doing that every week.
“We’ve been averaging 14 tackles missed – but I set my stall at single figures. That is why they have been doing extras in training this week.
“The boys know themselves and have come up and apologised – but I don’t want apologies, I just want good technique.”
Ex-Great Britain rugby league international Steadman made the move to BT Sport Cardiff Arms Park in the summer, having worked the last three seasons in England with Premiership outfit Newcastle Falcons.
And he revealed how much he is enjoying his new surroundings in the south of Wales.
He added: “I’m absolutely loving it here. I’ve done the four nations now and the city is a really lovely place and the people have made me feel really welcome.
“As a team, the pleasing thing is that through a tough period we’ve been competitive, apart from Zebre away. We’ve always been in a shout of winning it.
“We’ve come back from some tough away fixtures early on in the season and the group has always stayed close.
“The first time I came down here and saw the facilities I couldn’t believe the place,” he revealed. “There are no excuses and everything is set up for what is a quality working environment.
“I know Danny (Wilson) is setting his sights on changing a few things moving forward, but we know that takes time. Ultimately it’s a result driven business and at the moment we are on a run so long may that continue with good performances.”
Tickets remain on sale NOW for the European Rugby Challenge Cup clash with Montpellier. Call the Ticket Office on 02920 302030 or click HERE to buy online.