Allison left the Maranello outfit last summer after a three-year spell before committing to Mercedes following the departure of its own tech chief, Paddy Lowe.
The 49-year-old engineer actually had an input in the design of the Scuderia's victorious SF70H which outpaced Mercedes W08, and praised his former team's performance.
"If it wasn't already clear after qualifying, then it's certainly clear now [after the race] that this is going to be a season of very small margins," commented Allison.
"Credit to Ferrari, they had a very quick car and we just weren't quite good enough to stick with them.
"We won't panic. It's race one of a long season and we scored some very good points with both cars.
"We'll be determined to make sure those small margins go our way next time."
Ferrari appears to enjoy a strong package, but Mercedes has promised an "immediate response" next week in China.
In the red camp, the man who took over Allison's responsibilities last summer is anticipating a critical development race this season.
"It's on the track that you reap the rewards of your collective efforts over the winter," said Ferrari's Mattia Binotto.
"It was a busy period during which everyone doubled their energy and effort.
"We still have 19 challenges ahead of us and today's race shows how the slightest thing can make the difference between being in front or being behind.
"Therefore, we must continue to push as hard as possible on development."