The versatile Blues defender played a part in his side's 5-1 home victory against Barnet on Saturday and is looking forward to another positive result this weekend at home to Bury.
He said: "It was about time we got a result like the 5-1 win against Barnet, because we've all been working hard.
"I was happy with my own performance and I'm now hoping I can keep my place in the team.
"I would have taken 1-0 or any other winning score against Barnet, but 5-1 is good for the lads' confidence and it was great to get the three points.
"But I was disappointed that we conceded the goal towards the end of the match. I would have liked to have finished the game with a clean sheet.
"I think our win against Barnet will make people sit up and take notice. But we need to kick-on and go into the Bury game on Saturday full of confidence.
"Another home game gives us a big chance to add more points and get more of our fans to come and watch and support the team."
Roberts has made two starting appearances so far this term and has benefited from playing alongside experienced centre back Paul Linwood.
He said: "I've been working well at the back with Linny (Paul Linwood), but there's competition with Shaun Kelly and Paul Butler. If I keep playing well hopefully I can keep my place in the team.
"It's up to the gaffer where I play and I'll play wherever I'm told, but I prefer to play as a centre half.
"I showed I could play in several positions last season as a centre half, but I was also named as a midfielder and a left back in other matches."
His impressive displays in midfield last season attracted interest from one Premiership club and a number of Championship clubs.
City chairman Stephen Vaughan has been a firm believer that the club's future success will be driven by a successful youth development system.
He said: "Kevin's performances since he came into the first team have been outstanding, and the award of an improved and extended contract will hopefully act as a catalyst and example to other youngsters at the club.
"If they work hard and learn their trade in the correct manner, they will be rewarded.
"We awarded Kevin Roberts with an extended contract after seeing his progress and rewarding it accordingly. It wasn't a case of Kevin Roberts knocking on our door."
The Liverpool-born player is now under contract at Chester until June 2010 after he signed a three year extension to his deal in December.
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