Brazil international goalkeeper Alisson brilliantly denied Arkadiusz Milik in the second minute of added time with the Reds holding onto their 1-0 lead at home to Napoli on Tuesday .
And for Robertson there was no doubt Alisson's stoppage-time impact was decisive as Liverpool kept a vital clean sheet to progress.
"We knew we had to get a fast start and that's what we did," Robertson told BT Sport .
"At 0-0 they had nothing to lose and they threw up their centre-back. It was an unbelievable save from Alisson.
"But to get 1-0 up we were confident we would keep a clean sheet and thankfully that's what we did."
Midfielder Milner was equally effusive in his praise for the Reds goalkeeper and the team's performance in general.
"It was always going to be a tough game against a good team," Milner said. "We know what Anfield is about on European nights, the crowd were amazing tonight.
"I thought it was a really good performance, we knew we had to defend well and we defended really well from front to back.
"Unbelievable save from Ally [Alisson] as well. I think it was a fantastic performance all the way through."
While Alisson protected Liverpool's 1-0 lead, they were indebted to matchwinner Mohamed Salah at the other end .
The forward scored a sensational solo goal, finishing superbly through the legs of David Ospina after beating two Napoli defenders for strength and pace.
It was Salah's ninth goal in nine home appearances for Liverpool in the Champions League and proved enough to secure progression.
"He’s a different class," added Robertson. "It might not go down as one of his best goals because it’s not in the top corner but the strength to turn the defender and then the composure to finish.
"It was exactly what we needed, to get ourselves in front and then we knew we wouldn’t change the way we played. We had to press them, we had to chase them, and we did that all over the pitch.
"We knew what we had to do tonight and we’ve done it so we can look forward to who we get in the last 16."