The player himself submitted a transfer request last week but the Reds have rejected three bids from the Spanish giants, the latest worth around £114m, and the owners released a statement maintaining that Coutinho would not be sold.
Speaking on BBC Radio 5 live, Jenas said the Merseyside club's stance is like "cutting off your nose to spite your own face."
He added: "Coutinho has done brilliantly for Liverpool. Yes, they have helped develop him, but the fact is that now the deal of a lifetime has presented itself - not just for him but for the club.
"Once the owners started to get involved, though, it became about power. It's one thing it coming from the manager's mouth - there being a feeling that he shouldn't be sold - but now they are in a situation that sets a precedent for future deals."
Barcelona are after the 25-year-old following the departure of Neymar to Paris-Saint-Germain for a world record transfer fee of £200m.
Jenas adds that the timing of the deal is an issue.
"Barca have got themselves into this situation by selling Neymar when they did, and Liverpool have struggled to make the signings they wanted.
"If Coutinho goes now, they know they will be in an even harder position - because they failed with bids for Southampton defender Virgil van Dijk and RB Leipzig midfielder Naby Keita and there didn't seem to be a 'Plan B'.
"But what's also weird about this situation, and another reason why Coutinho probably feels hard done by, is that Liverpool have sold star players in the past - like with Luis Suarez and Raheem Sterling.
"We had something similar with Dimitar Berbatov when he left Spurs for Manchester United in 2008.
"If a player deserves to move on to bigger things, like Barcelona, it should almost be like: 'Thank you for everything, you've done brilliantly, now on your way."