Alexandre Lacazette and Pierre-Emerick Aubameyang both scored to haul the Gunners back from a 1-0 deficit early on in the game to give the scoreline a comfortable look.
Arsenal have the advantage heading into the second leg in Spain, but Emery urged caution, given that Valencia have an away goal.
"In the first leg, we wanted to get a good result, knowing that it would be difficult," Emery told BT Sport.
"After the first goal, our response was very good, with calmness and passion. We took our moments and the goals in the first half gave us confidence.
"We wanted to win and not to concede a second goal, but we also had to play. The third goal came at the end and for us it was important, but [the tie] continues to be 50-50.
"Valencia are a good team. They played with strong players defensively and in midfield. They're strong at set-pieces, they scored and we struggled with set-pieces.
"We'll continue to work on what we can improve, on what we can do better, but generally in the first leg, over the 90 minutes, we can be happy and proud of the players and supporters. Now we will prepare the same for the second leg because we know it will be very difficult."
Lacazette echoed his manager's sentiment, insisting that the tie is far from over, but reiterating the club's desire to lift the trophy at the end of the season.
"We know it's going to be hard [in Valencia] so of course getting as many goals as we could is better for us," Lacazette said on BT Sport.
"I had two more chances where I could have done better but thankfully Auba scored the third one.
"We conceded the first goal. We knew they were good on set-pieces and we have to be careful of that in the second leg. But the team showed good character and reacted well, and that's a good thing from tonight.
"We want to win the Europa League to go straight to the Champions League but also to win a trophy. We want to finish in the top four in the Premier League and if we can go to Baku [for the Europa League final] it will be special."