Celtic boss Martin O'Neill told BBC Sportsound: "I thought we started really brightly with a couple of good chances but we couldn't take them. We got a goal in front and there was a man sent off so you think we should be really comfortable.
"We conceded a really poor goal just before half time and it changes the complexion of the game with Hibs having something to hold on to and they defended very well.
"Iheanacho comes off the bench and wins the game for us, in a game you thought we would be comfortable but it was an edgy ending.
"We've played some really decent stuff but we had to defend towards the end. Of course there was an anxiety before the goal but we got there. It's natural there would be anxiety with our supporters and maybe with the manager too.
"We've just got to take each game on its merit. You can't control anything else."
Celtic now sit just below league leaders Hearts on goal difference before the Tynecastle side face Rangers at home on Monday evening.
The Celtic manager said he would be watching the game but says the most important thing from his side is that Celtic have won their game.
"What do I want for tomorrow? I genuinely don't know. We've won today so there's a bit of relief for 24 hours.
"Even if we win the three games at this minute, it doesn't guarantee winning the league. The margin of error is very small and it seems like I've been saying that for months. It is what it is."
