Despite cruising into a 3-0 half-time lead through birthday boy Manzambi and Jackson's clinical brace, Villa rode their luck at times as Zion Suzuki denied Vedat Muriqi and Oguz Aydin rattled the crossbar.
Evaluating his side's mixed performance after weathering a turbulent start to the campaign, Emery said: "We are delighted with the first win at home. Then how we played in the first half I was not so happy. They didn't score but Zion \[Suzuki\] played fantastic, they hit the crossbar.
"We wanted to control the match better. In the second half we were planning to correct what we didn't do well in the first half, and I think we did it. Then we tried to stop them and we scored three more. I don't think they deserved 6-0 but for us, it's important for us to achieve the first win at home and how we could manage the different players as well and the progression in how we stepped forward."
Assessing how his summer arrivals are gelling and outlining their push for automatic qualification, Emery added: "We must exploit the different aspects of our capacity and sometimes we can score through set pieces. Sometimes we can score through transition in high press. Sometimes we will score well in transition. I think we had different goals today and I can feel confident.
"I was confident before today but there is still a lot of work to do. Our structure is strong, but we need more time. We are progressively getting better, progressively getting the balance that we need and today we took one very big step forwards. And those three points for us in the table is important and we are being ambitious. We want to be protagonists in the Champions League."