But Treviso pushed the Blues all the way and only trailed by three points at halftime before the home team pulled away to win 33-18.
And Burnell was quick to put a lid on expectations, demanding his side demonstate their killer instinct in the red zone.
"We've got to make sure we're a little more clinical with our chances," said Burnell. "There's still times when we've got to get a bit more direction to our game.
"At the moment we are at about 75-80per cent.
"There are still crucial areas to work on. It's ten points, but we are not going to get too carried away.
"We are going to be realistic and keep our feet firmly on the ground."
The Blues turned to Burnell and backs coach Gareth Baber after long-serving boss Dai Young departed in the summer for Wasps.
And full-back Chris Czekaj, who won the man-of-the-match award against Treviso, says the club have been vindicated by their decision to give the reins to the coaching rookies
He said: "It's been a great start for us this season with the new coaching system.
"We're a really tight unit now with great team spirit and it's showing on the pitch now with two great wins."
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