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The Hoops boss is feeling the heat after managing just three wins in 10 games, and Snodgrass reckons there are reasons for concern.
But it's not only results causing alarm, with Snodgrass fearing Celtic's off-field turmoil has seeped into the dressing room and left O'Neill fighting to keep the wolves from the door.
Speaking to Europa League odds, Snodgrass said: "I'm seeing signs from Celtic that I've never seen before, not just performance-wise but with too much political chatter being made public. Celtic's strength has always been keeping things in-house, backing each other and driving forward together.
"It feels like board-level issues have crept into the squad, making it acceptable, it seems, to speak freely about negative tactical or internal matters. I don't like seeing it. The job at Celtic isn't just winning matches, it's winning titles. That's the standard.
"The main thing is to stop the talking and deliver on the pitch. They have a big game against Besiktas where they need a solid performance.
"Martin O'Neill's teams over the years were always solid. They're still top of the league, which is positive, but the high standards they've set in recent years mean expectations are huge.
"When you set those standards, people come for you, so you have to keep the wolves away from the door. We thought they'd turned a corner by beating Hearts, but losing 2-0 to Partick Thistle brings the questions back.
"Growing up watching Celtic's success, you know that facing adversity can actually be the making of a team. People feel they've left the door open for Rangers and Hearts instead of driving forward and pulling away.
"Seeing board-level matters reach pitch level is never good because it creeps into the players' minds. It creates a real challenge, but the only way to get everyone off their backs is to stick together and put in winning performances on the pitch.
"Every game at Celtic comes with huge pressure. The demand in Glasgow for both clubs is winning. They're powerhouses who hate losing. There's a specific demand to break down low blocks domestically, which is a different challenge from Europe.
"Celtic taking their domestic approach into Europe has been difficult over the last few years. Playing three games in seven days comes fast, so you have to rotate and manage the squad effectively rather than getting bogged down in off-field noise.
"You see Martin O'Neill using his experience to keep the players united through defeats because the games come thick and fast. Europe has been a test, but domestically, winning trophies is the absolute expectation."