The 25-year-old flanker was voted Munster's player of the year for 2012-13 on the strength of several outstanding performances, and having been selected for Ireland's tour to North America he is on the brink of winning his first cap - even if Penney does believe he should be on the British and Irish Lions tour.
"Rob would be a bit biased because he sees me every day, but it's great to have his confidence," O'Donnell said. "He's like that as a coach - he just wants you to go out and have a lash, and that's what I did this year. He backed me all the way."
O'Donnell added: "He's coached Richie McCaw so knows what the back row is about. He also played there himself.
"It was a real honour to get the player-of-the-year award at Munster. I didn't really think about what it meant until the awards night itself.
"When you hear the names of the lads who won it, you realise what a prestigious award it is. It meant a lot to me and was a great confidence boost."
O'Donnell hopes to make his name in the Tests against the United States and Canada as the squad prepares to depart Dublin on Saturday, with the first match staged in Houston on June 8.
"It will be a new experience for me. I've been involved in under-age tours but this is something completely different. It has a different feel to it," he said.
"Hopefully I'll be capped and everything will go well with me on the tour, but we can't take the United States for granted. They've pumped a whole lot of money into their sevens team, which is getting better and better.
"They have players who are based in Europe, so they have some quality guys who can mix it at world level. It will be tough. Canada will be the same - both are very direct teams who will be looking for a scalp."