Strachan won't write-off Celtic Champions League hopes
The Parkhead side succumbed to a late Oscar Cardozo goal in the Stadium of Light to see their dismal group stage record extended to 14 games without a win outside Glasgow.
"There was plenty of application and heart and on that we deserved a point but it was just tiredness that beat us in the end.
"But we are definitely not out of it. We qualified with nine points last season and at the moment the teams in the group have six, six, three and three.
"A point against Benfica would have been really excellent but we are definitely not out of it, you never know what can happen."
Strachan explained his surprise decision to rest talismanic midfielder Shunsuke Nakamura and drop in-form Scott McDonald to give Chris Killen his first Champions League start was with one eye on retaining the Clydesdale Bank Premier League.
He said: "It's a case of having just two fit strikers at the club at the moment.
"Scott is in terrific form but he has played all the games so it's a case of looking at the squad.
"As for Nakamura, I'm the manager and I can do that sort of thing.
"It's very unfair for me to tell you why I leave players out but it wasn't for his lack of ability or heart.
"But as a manager you sometimes have to made decisions and they understand where I am coming from.
"My priority is, as I've already said, is to win the Scottish league.
"If I can do very well in the Champions League then that would be exceptional but my priority is to win the SPL."