Slomka, who has led the club to their two most successful seasons on record, put pen to paper on a deal until 2016 on Saturday.
And after seeing his side defeat Bayer Leverkusen 3-2 yesterday, he explained his motivation behind committing to the club.
"We want to remain established in the top 10 of the Bundesliga," he said. "It's a bonus to be able to play in Europe.
"That is why we are hungry so that we can make it again next year that we play European games on a Thursday night, or better still on a Tuesday or Wednesday.
"It is our goal to keep working hard on achieving that."
Yesterday's victory lifted Hannover to within four points of the top three, a position which would earn them Champions League football after two seasons in the Europa League.
Slomka's new contract should ensure that continuity at a club who just three years ago were on the brink of relegation to the second division following the tragic death of goalkeeper Robert Enke.
"This was an important decision for the future of Hannover," said Slomka to Sky television.
"It's extraordinarily good that the club have placed their faith in me for the coming three years after the successful recent times.
"It was a very harmonious agreement and everything was right for both parties - we are a perfect match."