Tilson guided the Shrimpers to five win from as many games this season, scoring 15 times and conceding just six as they joined Swansea at the top of the table.
He said: "It's been a good month, obviously five wins out of five speaks for itself.
"I may have been named manager of the month but the players are the ones who've gone out and got the results, they've been brilliant."
The Shrimpers face Nottingham Forest on Sunday looking for a record breaking win. If they claim all three points it will be their eighth successive League victory, and set a new club record.
Wycombe boss John Gorman won the League Two award, with Sheffield United's Neil Warnock taking the plaudits in the Championship.