The Shrimpers were sunk by first-half goals from Neal Trotman and Adam Lallana (2), and although George Friend replied with a fine free-kick, Tilson's men could not avoid defeat.
"It was a good effort from the lads but if you give away goals against a good side then you will get punished," said Tilson.
"We conceded three and it was always going to be an uphill struggle but in the second half we controlled the game.
"If we had done that in the first half then who knows what might have happened.
"There was nothing wrong with the performance and there were a lot of positives, but now it is about moving on."