In order for your systematic review to be reproducible, it is important to keep track of the search strategy you use for each database. That way, someone else can verify your research.
Furthermore, a spreadsheet helps you keep track of the total number of duplicates for your project as well as the number of duplicates from each database searched.
Finally, PRISMA recommends you report at least one search strategy in your published manuscript, so keeping track of it in a spreadsheet will help you when you write your manuscript.