A brace from Bertrand Traore and goals from Kasper Dolberg and Amin Younes saw Ajax take complete control of the tie with their win in Amsterdam.
Bosz said his side's ability to take their early chances set them up for a crucial home win.
"It was an odd game. I thought that we were pretty bad in the first 15 to 20 minutes. Lyon put us under pressure and we weren't able to play. It looked like we were tense," he told a news conference.
"But in contrast to what we've been doing all season, we converted our first two opportunities. We were suddenly up 2-0.
"In combination with the fantastic crowd, something beautiful happened."
Traore and Dolberg struck in the first half for Ajax before Younes stretched the lead shortly after the break.
But Mathieu Valbuena pulled a goal back for Lyon before Traore's 71st-minute sealer.
Bosz knows his team are well-placed, but is wary of Lyon ahead of next week's return leg.
"We are in a great position, but the first 20 minutes – in which we played poorly – have taught us that we're definitely not there yet," he said.
"We'll need to give another top performance in Lyon in order to reach the finals."