Burton missed out on a place in League One next season courtesy of a 1-0 defeat in the playoff final today, with Lyness at fault for the only goal of the game.
However, Rowett insists that he can't feel too disappointed at having fallen at the final hurdle after enjoying an impressive season on the whole.
"I told him to get his chin up. Unfortunately, sometimes a mistake dictates a result, we've seen it in the playoff games and in the Champions League final," Rowett is quoted as saying by PA.
"I can't be disappointed with him, he'll be disappointed enough for himself. Maybe he took his eye off it, but I'm not going to berate my keeper. I can't be downbeat after the season we've had. I'd have rather lost here at Wembley than at Southend last week.
"And we were in the wrong dressing room. Apparently all three losing finalists were in the home dressing room, so I'm blaming whoever makes that decision!"
The result means that Fleetwood have now secured promotion six times in the last nine years.