Former Liverpool strker Peter Crouch revealed Reds goalkeeper Alisson had to tell the crowd at Anfield to 'calm down' as a nervy atmosphere set in.
Liverpool went ahead in the 11th minute thanks to Alexis Mac Allister as he timed his run to perfection and slotted home a cross from Mohamed Salah.
However, Arne Slot's side slowly lost their grip on the contest as Bologna had more success going forward.
The Serie A side even hit the woodwork in the 30th minute via Dan Ndoye as Dominik Szoboszlai failed to clear his lines.
With Bologna coming agonisingly close to an equaliser, the atmosphere in Anfield became rather tense.
Alisson had a two-word message for fans at Anfield after Bolonga crept back into the game
But Alisson, often a presence of calm at the back, wanted fans to settle down.
Speaking on TNT Sports, Crouch revealed the Liverpool goalkeeper's act and discussed where the host side was starting to go wrong.
'Liverpool were in total control and they've (Bolonga) just come back into it,' Crouch said.
'It's a little bit of shooting themselves in their own foot, really. They're playing out from the back and getting caught with it. Bologna is getting chance after chance.
'Alisson's just told the crowd to calm down because you can sense around Anfield it's getting a little bit nervy. What happened with Atalanta, there's a bit of history there. Liverpool need to regain control.'
Crouch's reference to Atalanta was when Liverpool dominated possession against the Italian side in the first leg of their Europa League quarter final last season but had nothing to show for it.
Atalanta proved to be ruthless on the counter-attack as they went on to win 3-0 at Anfield.
Liverpool won the second leg 1-0 but it was not enough to avoid elimination.
The Reds are hoping to make it two wins from as many games in the Champions League this season.
Slot's side got their continental campaign off to the perfect start in September when they beat AC Milan 3-1 at the San Siro.
Goals from Ibrahima Konate, Virgil van Dijk and Szoboszlai did the business as they came back to win after Christian Pulisic gave Milan the lead in the third minute.