The Leicester Tigers scrum-half was initially part of Warren Gatland's squad but withdrew after the wife of Youngs's brother Tom was diagnosed with terminal cancer.
However, while Cole backed his teammate's decision not to tour, he indicated that the 27-year-old will have the chance to wear the Lions shirt again.
He told Sky Sports News: "As a player you realise these things (tours) are rare and you are always gearing for the next one after the last one finishes.
"So for him to give it up shows the importance of family and underlines the fact that there is stuff bigger than the game. Ben has made a decision and everyone stands behind him and it is the right decision to make.
"He's young. He's only 27, there is still plenty of time for him. There are 31-year-olds in the squad and I'm sure there are people who have played for the Lions when they are 35."
Youngs was replaced in the Lions squad by Scotland captain Greig Laidlaw.