At one point, the 30-year-old had been tipped to captain the side - an honour that went to Wales player Sam Warburton.
But the hooker was left out of the 37-man squad announced by Lions manager Andy Irvine, with spaces instead for England's Dylan Hartley and Tom Youngs alongside Wales' Richard Hibbard.
The Co Armagh man's teammate Tommy Bowe made the cut, alongside fellow Ireland players Rob Kearney, Jonathan Sexton, Cian Healy, and Jamie Heaslip.
"To get the call, it's given me a huge boost to the confidence," Bowe told UTV, during a trip to Belfast Zoo to feed the lions.
Best took to Twitter to Tuesday evening to express his disappointment, but also tweet his congratulations to Bowe - adding that all the "hard work getting back from the injury has paid off".
Head coach Warren Gatland, who also failed to name England's Jonny Wilkinson and Chris Robshaw, said the decision had not been taken lightly.
"There was a robust debate about the squad and there were healthy discussions for every position.
"Some real quality players have missed out. We had a thorough process and it's been tough."
He did offer hope to those left out, however, saying: "If you look at previous tours six to eight players get injured and there will be a group of back-up players who can be called upon."
Brian O'Driscoll is also among the nine Irishmen on the full squad for his fourth tour, alongside 2009 captain Paul O'Connell.
At just 24, Warburton is the youngest Welsh Lions captain in history and he has bounced back from injury sustained in this season's Six Nations to lead the tour.
Two years ago, the Cardiff Blues flanker captained Wales into the World Cup semi-finals, in which his side gave their best performance in 24 years.
And while rugby fans were speculating over who would take the top spot, Warburton admitted he had known about the news for some time.
He said: "Warren gave me a call, it's been nine or 10 days since I found out and the biggest secret I've had to keep.
"It's unbelievable, an accolade very few people achieve and it's an unbelievable honour."
Gatland's squad is split into 16 backs and 21 forwards and, four weeks from Tuesday, the party will leave for Hong Kong where they open the 10-match tour against the Barbarians on 1 June.
The Lions then head to Australia with the first of three Tests against the Wallabies in Brisbane on 22 June.
L Halfpenny, S Hogg, R Kearney, G North, A Cuthbert, T Bowe, S Maitland, B O'Driscoll, M Tuilagi, J Roberts, J Davies, J Sexton, O Farrell, C Murray, M Phillips, B Youngs, G Jenkins, C Healy, M Vunipola, A Jones, D Cole, M Stevens, D Hartley, R Hibbard, T Youngs, I Evans, R Gray, AW Jones, P O'Connell, G Parling, T Croft, T Faletau, J Heaslip, D Lydiate, S O'Brien, J Tipuric, S Warburton (capt).