By saying "Now the synthesis timing report showed all paths met timing", you are conflicting yourself's statement that "I missed by mistake to constraint only one path which was an path from an input to a flipflop".
Logically, we can draw the conclusion that your "synthesis timing report" is not exhaustive or complete enough for sign-off.
A well-architected synthesis flow should have timing reports(or warnings) on paths that are "UNCONSTRAINED".
If you don't have a methodology for synthesis flow, you need to create your own script/tcl to tell the synthesis tool to generate timing reports for input/output related path.
When you get the reports, search for "unconstrained" and you'll get it quickly.
In addition, SDC is one of the most important deliverables designers own. Missing an input constraint is a huge mistake. You should take this as a serious lesson.