The Rams clinched a 2-1 victory at Brighton before a crowd of 26,238 at the Amex thanks to Martin's brace following Leonardo Ulloa's openinggoal for the Seagulls.
Martin was with the Rams on loan last season and moved on a free transfer and an enthused Clough said: "He is the one that we are most pleased with.
"It's very important for him to get a few goals as he is our main target man.
"He did well while on loan and needs a home with us. Hopefully he'll stay with us a few years and help us achieve what we want to achieve."
Clough also insists there is "nothing wrong" with aiming high and says his men are striving for the top six after several mid-table finishes.
He added: "We believe we are as good as anyone in the league. We have got to get confidence through to our young side to help with the belief that we are as good as other teams."
Clough was especially delighted to achieve a win in his side's first away league game, as the Rams only won four matches on their travels during the whole of last season.
He said: "There was a bit of everything in our performance. The way we started pleased me the most and we controlled the game for long spells.
"We didn't deserve to go behind and once we had taken the lead we had some good situations ourselves."