Warburton has struggled to recapture his best form this season, and the performances of stand-in skipper Jones and Justin Tipuric in the victory over France in Paris meant interim coach Rob Howley did not even wait to discover if Warburton had recovered from a shoulder problem before making his selection.
When asked if he had ever felt he did not want to captain Wales during his own struggles with fitness and form, he said: "I would be lying if I said no, but you have to realise I hold it in such high esteem I would never say I did not want to do it."
Jones does not believe Warburton is feeling the weight of being the favourite to lead the Lions when they tour Australia in the summer.
"In 2009, maybe the talk of the Lions captaincy did have an effect on me, but all players know the captaincy will take care of itself. It will depend on who is going, the make-up of the team... It is not something you can control.
"It's not like a job you apply for, it's an added bonus for the person who gets it, that's what I would tell Sam."
Jones added of the captaincy: "It means the world to me and it is only when you lose it you realise the value of it.
"The most difficult thing is when you are going through personal turmoil.
"It is easy to be captain when you are winning and playing well. But if you are losing, or you are winning when you are not playing well your position is called into question.
"That's difficult because you are concerned with your natural standing among the group, but it becomes easier with age. You have life experiences other than just playing, it is easier to add value in other ways."