The hosts fought back from going an early goal down to beat the Premier League outfit 2-1 amid frenzied celebrations at their 10,000-capacity stadium.
Boel, 38, said going up against Unai Emery made the win even more special.
"This isn't just any manager you beat, and for me it's a dream to stand next to him, and even beat him," he said at the post-match press conference.
"We had nothing to lose. Of course, we knew it would be incredibly difficult. But there always has to be faith. No matter how small. You don't have to give up until the very last whistle. We tried to hold on to that little bit of faith."
Go Ahead Eagles won their first trophy in 60 years last season with a surprise success in the Dutch Cup, but Thursday’s victory is being hailed as a much bigger feat.
"As a coach or player, you’re fully focused on the game, thinking about what still needs to be done and what adjustments to make," Boel added.
"But after the final whistle, you look into the stands and see big men hugging, crying, and celebrating. This is something the club and the city will remember for a long time.”
Captain Mats Deijl, whose storming run from his right-back position saw him score the second-half winner, said they knew it would be a tough task to beat the Premier League side but they maintained belief in themselves.
"The charm of football is that you never know how things will go,” he added.
After beating Panathinaikos in Greece earlier this month, the Dutch minnows now have an unexpected six-point haul.
"People assumed we wouldn't get many points, if any. I don't blame them, and secretly it wasn't exactly what we were expecting either. But the fact that it turned out this way is wonderful," Deijl added.