Amo-Ameyaw, 18, secured all three points for Liam Rosenior's side, seeing them move up to fifth in the division, when he converted from close range on 89 minutes.
The England youth international joined Strasbourg on loan with an obligation to buy in the winter window, much to the frustration of supporters.
The BlueCo-owned club - the same ownership as Chelsea - will pay Saints nearly ā¬10million (around Ā£8million) to sign him permanently this summer.
Fans have further questioned the decision to sell the talented teenager since witnessing his impressive early performances in France.
Amo-Ameyaw scored his only Saints goal against Cardiff City.Amo-Ameyaw scored his only Saints goal against Cardiff City. (Image: Matt Watson / Southampton FC) READ MORE: 'Great technical ability' - Amo-Ameyaw praised after Ligue 1 debut
Technical director Johannes Spors, who was not at the club when Amo-Ameyaw was sold, recently admitted he would not have allowed the teenager to leave.
"It was a decision that was taken, so I respect it, but if you ask me now, I would prefer to see them playing with our jersey - you can always sell later," he told the Daily Echo.
Southampton's loss is Strasbourg's gain, and asked about his maiden goal for the in-form Ligue 1 club, Amo-Ameyaw said: "It's an amazing feeling to score my first goal.
"Most importantly, we got a win for the team. I'm very happy. You can see how together we are. I feel like the vibes help on the pitch as well."
Amo-Ameyaw had to be patient following his switch to France but has featured in Strasbourg's last two games.
"I just carried on training well. Last game, Dilane Bakwa was suspended, so it was an opportunity for me to show what I can do.
"I think I was able to do that. I just take things step by step, keep training well and hopefully, I can get myself in the team by working hard.
"It's crazy. Lyon is a very good team, but we responded in the second half. When I came here, I was very shocked at how together everyone is.
"Everyone here is very close, they are all friends. Everyone speaks to everyone."
Amo-Ameyaw departed Saints, having seen his first-team involvement reduced heavily under Ivan Juric.
The former Spurs prospect admitted it was difficult to impress the Croatian manager after he was moved back to the under-21s.
Since moving to France, Strasbourg boss Rosenior has backed the youngster and praised his "great technical ability".
On social media X, Saints fans said:
#SaintsFC should never have put themselves in a position where they were forced to sell Sam Amo-Ameyaw and Jayden Meghoma. š
ā Just Saints (@JustSaints_) March 28, 2025
š
ā SaintsFC_Youth (@SaintsFC_Youth) March 28, 2025
https://t.co/3D7C7W8Pxm pic.twitter.com/NSg3TysAYN
ā Dylan (SR Out) (@PlayzytStyle) March 28, 2025
š¢š¢ https://t.co/ypr9sXEAOR
ā cr (@999999999cr) March 29, 2025
Sam Amo-Ameyaw. pic.twitter.com/1NRh6JkeMq
ā Gšš½āāļø (@Gknowsball) March 29, 2025