The Pilgrims were well aware of the daunting task that awaited against a Liverpool side second in the Premier League and 68 places higher in the football pyramid, though Jürgen Klopp made no secret of his intentions to name a second-string team.
The Reds boss did just that, naming the youngest line-up ever seen in the club's 125-year history, but despite all their youthful promise - were kept at bay with their best chances both going begging through teenage forwards Sheyi Ojo and Ben Woodburn.
That meant that the two sides will go head-to-head again within a fortnight in a replay at Home Park, with Adams delighted with the performance on offer from his players on Merseyside.
We worked "extremely hard" and did "really well", insists jubilant Adams
"I think it's probably one of the best defensive performances that Anfield has ever seen," he raved afterwards to reporters.
"We defended deep and defended in numbers. We've allowed Liverpool to have the ball and that was our game plan. You've got to stop good players from having space and time and that's what we did today.
"We wanted to win the match, we thought we'd have a couple of opportunities in the game throughout the 90 minutes. We did have a couple of opportunities, [but] we didn't take them.
"We limited Liverpool to not many. They got into wider areas to put crosses in the box, we dealt with them well. I think the players have worked extremely hard today."
The Scot continued: "It was about negating the space. We didn't allow them to have space. We allowed them time, at times, to be on the ball and move it but they didn't open us up.
"We doubled up down the side. We were very good defensively and it'd be naive as a manager to come to Anfield and think that you can go at top-class players.
"From my point of view, we worked on it and the players did really well at that."
Adams: Liverpool had few shots on target and that's a credit to my players
Liverpool enjoyed 76 per-cent possession overall on the afternoon and fired 28 shots on goal, although a mere four tested goalkeeper Luke McCormick - who was only called into significant action on a few occasions.
Adams, 41, added: "They could have had 90 per-cent possession if they wanted, the game plan was to not allow them to score. That's what we did.
"We've come to Anfield, I think there's only three teams that have come here and drawn 0-0 in recent times, and Plymouth Argyle are one of them.
"We're a League Two club, they're a Premier League club. They've got multi-million pound players, they had multi-million pound players playing today. They've got players that have played at international level.
"They had enough on the pitch to beat Plymouth today but sometimes they came up against an opposition that are stubborn and have got a work ethic and good legs and can take the ball in at times as well.
"This was about a team performance. We had 13 players playing today that all deserve a huge amount of credit because it's not an easy venue to come to.
"The result will tell you that we coped well because we limited them to not many opportunities in the game.
"They had a lot of possession but did they have many shots on target? The answer to me is no. I didn't see many. That's a credit to our players."
Home Park replay will be a welcome to the real world for Liverpool, says Argyle boss
Asked what awaits Liverpool in the return leg in Devon later this month, Adams believes the Reds will get a proper glimpse of the standards of lower league football.
He said: "It's not as luxurious dressing rooms as they are here, even though we're in a port-a-cabins. From that point of view, welcome to the real world.
"Liverpool are a very good team. Will they change things for the next game? I'm unsure.
"We will have to be very good defensively as we were today. Yes we'll have to open up a bit to get through to the next round but the main purpose of today was to try and win the match.
"If we couldn't win it, then [the aim was] to take them back to Home Park. We've had a fantastic day today, we'll have a fantastic time in the replay."
Broken ankle or ligament damage for Miller
The only thing marring an otherwise memorable day for Plymouth was a nasty-looking injury to defender Gary Miller, who had to be stretchered off and given gas.
Issuing an update on Miller, Adams said: "[He's] Possibly got a broken ankle or ankle ligament damage. He's going to hospital to get an x-ray. We'll wait and see the extent of his injury.
"I believe he went up for the header and came down. I'm not sure if he made contact with a player on the way down or not, I haven't see the video footage. But I'm told the footage doesn't look good.
"We'll obviously know the full extent over the next couple of days."