The Rams ended an eight-game winless Championship streak with a 3-1 comeback victory at Brentford on Saturday.
Martin came off the bench with the Rams trailing 1-0 and helped create one goal before scoring the third - just his second goal in 19 games.
"It's nice to finally contribute. I feel a lot lighter with that monkey off my back," Martin told BBC Radio Derby.
"I have been a bit non-existent for the last couple of months."
The 27-year-old's strike was his 10th league goal in 31 appearances, but only his second since finding the net against Huddersfield Town in October.
But Martin said Derby would not be over-reacting after earning their first league win this year. Their last victory was a 2-0 success over Fulham on Boxing Day which took them top of the Championship table.
"It's not a time to celebrate and dwell too much because the win should have come much earlier and we understand that," Martin said.
"I don't necessarily think I am not contributing if I don't score, but the big thing is I want to contribute to winning performances and we hadn't managed to win in a long, long time.
"The main feeling is elation and relief at winning the game. But it's not a time to really celebrate.
"But this is a great lift. We have started the week extremely well and hopefully we can kick on again."
Derby are at home against Blackburn Rovers on Wednesday and away to Wolves on Saturday.

The South Africa-born 23-year-old had been playing club cricket in the East Anglian Premier League this season.
"Sean shows a great maturity with the bat and understands his game well," Kent's high performance director Simon Willis told the club website.
"The number of runs he has scored in all formats is testament to his focus and concentration."
Dickson, who has a British mother and holds a UK passport, has previously played first-class cricket for Northerns in South Africa.
He also bowls medium pace and could make his first-team debut for the club in their T20 Blast match against Glamorgan on Friday.
Kent have not disclosed the length of his contract at the St Lawrence Ground.
Striker Chris Martin has described his input during Derby County's dismal recent run as a "bit non-existent".
[NEXT_CONCEPT]
Kent have signed batsman Sean Dickson after he impressed during a trial spell with their Second XI.