The Dutch side sealed a narrow win over the Premier League outfit in London thanks to Donny van de Beek's goal after 15 minutes.
The crucial moment came during Ajax's brightest spell in the game as Tottenham became more of a threat in the second half.
Although he admits his side struggled to keep possession after Spurs changed shape to cope with Jan Vertonghen's injury, he was delighted with the performance and expects even better in the next game.
"It's a great achievement. We've fought like lions," he told Ziggo Sport. "In the first part, we played very good football and the goal was deserved. We dominated but after a while we failed to play football.
"In that phase we had more chances as we could have scored more. Nevertheless it's a good result."
"We didn't anticipate well after the substitution [of Jan Vertonghen]. We weren't able to keep the ball and that made it unnecessarily hard. We had to follow the ball too much.
"Tottenham chose a more opportunistic style and it cost a lot of power to keep the pressure on them. We would have loved to have the kept ball a bit more, but then we had to change our system, which would have made it easier for them to avoid the pressure.
"I'm sure Tottenham has gained insights from this game, but so have we. We are halfway through, that's how you should say it. We have a good starting position, but it should be better next week than it was today. I'm very satisfied with our progress and growth."
The coach also highlighted midfielder Van de Beek's performance, saying he did more than score the crucial goal.
"He played incredibly well. In the final phase he was important, but also defensively. He covered incredible ground and won many duels and second balls."
The two sides meet again in the second leg in Amsterdam on May 8.