The Imps went into the final day knowing victory would ensure their safety, but they slipped a defeat which, coupled with Barnet's 1-0 victory over Port Vale, meant they fell out of the Football League.
Lincoln's problems started when veteran Jamie Clapham felled Jermaine McGlashan in the area after 57 minutes, allowing Danny Hylton to net from the spot.
Luke Guttridge then added a brace to send the Imps to the Blue Square Bet Premier, much to Tilson's dismay.
"When I came in I knew it was going to be a tough job but I thought we'd done enough to be safe," he said. "We simply weren't good enough.
"The league table doesn't lie. It's not just this season. It has been the last three or four years that the club has been battling against relegation."
Source: PA
Source: PA