Jurgen Klopp's men are top after extending their 100 per cent record thanks to a 2-1 win over Eintracht Frankfurt, with Mkhitaryan scoring his first two goals for the club.
The Armenian, a close-season acquisition from Shakhtar Donetsk, believes both he and his team-mates will continue to improve as a unit.
"It's not really me you should be congratulating but the team, it's most important that we won," he told the official Bundesliga website.
"I'm really settling in, this is a great place to improve, and we're still getting better as a team. Jurgen Klopp is one of the best coaches in the world, and I'm proud that he's my coach - together we can be successful."
The victory was Dortmund's first at the Commerzbank-Arena since May 2009, having not won in three attempts prior to Sunday's clash.
Goalkeeper Roman Weidenfeller believes the timing of Mkhitaryan's goals, 10 minutes into the first half and 11 into the second, was crucial.
"It was a tricky game and Frankfurt were excellent - thankfully the goals came at important moments.
"I think the best team won though. Frankfurt closed down the space well, which meant we moved the ball slower than we would have liked. Being top of the league with twelve points is the most important thing - we've started well."
‘Managing Leeds? It was an option that appeared, but it wasn’t the right timing. I decided it wasn’t a good idea to leave the club I was at mid-season’: Premier League boss admits to turning down opportunity to replace Jesse Marsch in 2023
‘Ruben Amorim could have waited for Real Madrid and had a better chance to be successful – to have joined Manchester United, he must be convinced in his own ability’ Former Old Trafford coach’s verdict on new boss
