The Cowboys may have been well below their best in a 20-16 loss to the Eels but they also know they need to come to grips with the fact that every side they play will lift in an effort to get a win over the 2015 premiers.
Speaking after the narrow loss, co-captain Matt Scott said he expected sides to go to another level against his team every week from here on in.
"There's going to be a bit more pressure on us, teams are going to lift to play us and we have to handle that pressure a bit better," he said.
But he added the Cowboys made life hard for themselves with a stack of errors and ill-disciplined penalties to gift the Eels attacking chances and said if they can rectify that they'll make life harder for opponents in future.
"I think if we hold the ball then it's a totally different game, we take energy out of them, they don't have as much energy in defence and we have more, it's a pretty simple matter I think," he said.
He also refused to blame a hefty pre-season travel toll that included the full NRL squad travelling to Auckland for the Downer Nines (even co-captain Johnathan Thurston travelled, though he didn't play) as well as a trip to the UK where they won the World Club Challenge over Leeds.
"Physically, energy-wise we're good. The hardest aspect of the game is defence and defensively I think our attitude was really good [against Parramatta]," he said.
"A couple of soft tries we need to be better at but physically against a big pack we did well. Concentration let us down, simple errors."
Eels skipper Kieran Foran confirmed his side treasured the win even more as it came against the best side of 2015.
"I guess there's that added motivation; you know you're coming up against the defending premiers and a quality side," Foran said.
"The Cowboys have got strike all over the paddock and they've also got the world's best player in Johnathan Thurston. So you have to be on your game and you have to be on defensively."
The Cowboys have a chance to get their premiership back on track when they host a desperate Roosters side sitting on a 0-2 record next Thursday night in Townsville.