The Reds boast victories against Sheffield United, Coventry and Preston in their debut season in League One, without conceding a goal, and Barker believes this speaks volumes for the progress that they have made.
He said: "It's fantastic that we've beaten clubs like that. The challenge for us now is to do it on a regular basis.
"We've got an opportunity now to reach 70 points and finishing as high as seventh. We've won three of our last four games and want to make it four out of five in our final game at home to Hartlepool on Saturday."
Barker admits he may face a battle to hang onto some of his best young players as rival teams look to strengthen for next season.
He added: "We've got some good young players that are worth money. If I were a manager wanting players I would watch us. We have got a fantastic bunch of players who work hard. I think most of them could play in the Championship."
Barker was delighted with the way his men bounced back following a 2-1 defeat at Oldham last Saturday and said: "It would have been easy to feel sorry for ourselves but I was extremely pleased with our attitude. Over the first 45 minutes we were excellent."
This was Preston's first defeat in five games and manager Simon Grayson felt they paid the penalty for a poor first half.
He said: "I'm disappointed because I didn't want us to go down with a whimper. We started very poorly, were not lively and didn't press them. We allowed them to dictate.
"In the second half we showed more energy, dominated and were more lively. A draw would have been a fair result, I think. We hit the bar through Jack King and could also have had a penalty as Nicky Wroe felt he was held back."
- Sports & Recreation