The Italy forward arrived at Signal Iduna Park in the close-season but has found his playing time somewhat limited in the early throes of the campaign.
However, the 24-year-old gave a timely reminder of his quality with the first goal in Dortmund's 2-0 victory over Arsene Wenger's men in their UEFA Champions League Group D opener.
And the former Torino man believes there is more to come.
"It was a very, very important strike for me," he told reporters. "I'm relieved.
"Everyone at Dortmund has been waiting for me to score, people expect me to notch goals. This goal will boost my confidence and help me trust my skills.
"It will make me even stronger and hungrier in the coming weeks. It was a very important goal for the team as well in terms of the next few games."
Immobile also feels that the goal will help convince any supporters who may have had reservations over his talent.
He added: "The fans gave me a huge applause on my substitution and I really enjoyed that, although I'm sure there were moments when some of the people will have had doubts, as I'd failed to find the net in previous games.
"That's football, though. I'd been dreaming of playing in this stadium in front of these fans and wearing this shirt, and after a game like this, it's easy to see why."
