The clash at the Allianz Riviera finished all square due to Donny van de Beek levelling matters in the 49th minute, following Mario Balotelli’s opener in the 32nd minute.
The result means Nice will have to win the second leg in Netherlands, but Favre believes they have what it takes to pull it off.
“Anything is still possible. Now, it’s clear, we will have to score over there next Wednesday,” he said, according to the official Ligue 1 website.
“I’m fairly satisfied with our match; I though we were pretty solid and we didn’t let them play their game all that much.
“The equaliser hurt us a fair bit. A tactical slip-up led to that goal; we couldn’t manage to stay focused and disciplined enough in the second half and we allowed Ajax too much space.
“When this team manages to start finding [striker Kasper] Dolberg and the midfielders, things get complicated. But we could have made it 2-1 with a number of counter-attacks.”