The Leith outfit battered Gers from start to finish but still managed to come away with nothing as the visitors’ smash-and-grab display claimed a 2-1 win.
Lewis Stevenson fired Hibs in front early but goals from Josh Windass and Alfredo Morelos just before the break swung the game back in Rangers’ favour.
It was one-way traffic as the second-half resumed but the hosts failed to find the breakthrough.
Lennon was left seething after referee Kevin Clancy failed to spot what he thought was a “blatant” penalty-box handball by David Bates with 15 minutes left, while there was further frustration as wideman Barker hit the post twice among a series of chances that went begging for Hibs.
“It’s worse losing like that,” said on-loan Manchester City youngster Barker. “I’d rather get beat 4-0 than lose a game like that. It was horrible.
“We dominated the game from start to finish, especially the second half when we were all over them from the first whistle.
“It’s just one of those days and at the minute it just seems like we’re not getting that slice of luck that we need. Hopefully that luck will come soon.
“Look at the penalty claim. It was a stonewall but the ref obviously hasn’t seen it. Again that is that bit of luck we’re missing. We needed the ref to give that to get us back into the game.
“But I’m not going to moan and say we should have got a pen because we could have scored (before that) and won the game 4-2.
“It’s annoying when you don’t get a decision like that but the game, in our opinion, should have been dead and buried before that.
“I decided before the game to shoot as much as I could but ended up hitting both posts, which is gutting. The keeper has made an unbelievable save on the second one. But I’ll just need to go again and shoot some more on Saturday.”