Rowntree said the 26-year-old was disappointed to have been left out but insists the door is not completely closed for the flanker.
"He was upset and quite rightly so, he's been exceptional for England," Rowntree told BBC Radio 5 Live. "There's going to be injuries and Chris will be one of the first names we turn to. He's desperately unlucky."
An injury call-up may also be possible for 2003 World Cup-winner Jonny Wilkinson, who turned down a place in the 37-man squad as he is committed to finishing the season with French club Toulon - which would have meant he would miss early games of the tour.
Lions head coach Warren Gatland has selected only two fly-halves - Ireland's Jonny Sexton and England's Owen Farrell - which offers a glimmer of hope to Wilkinson.
"We'll consider that as when we need to with injuries," added Rowntree.
"People talk about our reserve list but we'll deal with that with each instance, seeing who is available and who is in form around the world."
He added: "We've not left it (Wilkinson's spot) vacant, we think we've got cover there for an emergency 10."
Gatland's selection has been criticised in Australia as being one-dimensional, but Rowntree denied that, saying: "We want to play different games, a power game and a quick game. I think the squad represents that nicely."
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