However, he refused to comment when asked whether he thought their style of play would get them out of the division.
Crawley went ahead at the Broadfield Stadium against former boss Steve Evans' Rotherham through an early strike from Mat Sadler, but goals from Kieran Agard and a first goal for the club by substitute David Worrall secured the Millers maximum points.
Barker said: "With what they have at their disposal I would expect them to be around the top six. But in this game there was two contrasting styles.
"We're not going to win the league, but let's try and play the right way. I want people to be entertained."
Former West Brom defender James Hurst was punished for an error in the build up to Worrall's winner, but Barker refused to be over-critical of his young side's defensive failings.
He said: "Individual errors cost you at whatever level. Mistakes can be ironed out. We can't sign players who've had 300 league games - we have to produce our own."
Barker admitted that it "didn't get much harder" for his side with successive away games at Wolves and Peterborough, but added: "For Crawley to be competing at Wolves shows we've come a hell of a long way.
"Our players will thrive on that. We've had three games and part of it is a learning experience for the players. We need to show people what we can do."