The Dens Park side have had a mixed start to the season, winning 4-0 at Kilmarnock on the opening day then losing 2-1 at home to Hearts at the weekend.
Although they lost out to Robbie Neilson’s newly-promoted team, Dundee made several chances in the first half and could easily have won the match.
They are now preparing to visit city neighbours Dundee United in their first Tayside derby of the season on Tuesday night, live on Sky Sports.
And Hartley is convinced his side can build on the progress made last season on their first campaign back in the top flight of Scottish football.
Speaking to Sky Sports News HQ, the Dundee manager said: “We’ve started the season well and we’re enjoying our football and hopefully we can get another good result tomorrow night.
“We just want to try to improve as a group and a club. Off the park, everything is good and on the field we are getting better.
“We finished sixth last year and we want to try to improve on that. We’ve got a really talented group of players there and hopefully we’ve a good season ahead.”
Dundee won their first derby in more than a decade when they defeated United 3-1 at Dens Park in April.
Hartley is keen to give his side’s supporters something else to smile about as they bid to become the city’s leading team.
The former Scotland international added: “That was a great night. I think it means everything, especially to the supporters.
“They want the bragging rights and I think that was our first derby win in 11 or 12 years. We want to try to do that again but we know we’re up against a very good Dundee United team.
“I think it’ll be frantic. It’s like all derby games – we want to try to pass the ball and I expect a good game.
“We’ll need to play well and be organised, disciplined and focused. I believe in the group of players we’ve got.”
Watch the Dundee derby live on Sky Sports 1 HD from 7.30pm on Tuesday night. Catch the match for £6.99 on NOW TV. No contract.