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Jake Jervis hit the post in the second half, after Graham Carey and Paul-Arnold Garita had both gone close.
Liverpool went through with a rare goal from Lucas Leiva, ending an FA Cup run which has been worth £1m to Argyle.
"We were really unfortunate to go out of the cup because we had the opportunities to score," Adams said.
"We had to twist, we had to push forward and the players did that really well," added Adams, whose side had held Liverpool to a 0-0 draw with a very defensive display at Anfield 10 days earlier.
"We've got a lot of creative players in our team and at times we were in and around the penalty area. Could we have scored and seen the pressure that would have put on Liverpool?"
More than 17,000 people watched the game at Home Park, making it Argyle's biggest attendance for nine years.
"It was a fantastic atmosphere, it started really early and just got better as the evening went on," said Adams.
"The supporters sang their hearts out and the players responded to that."
League Two side Plymouth were unlucky not to progress in the FA Cup after their 1-0 replay loss to Liverpool, said Argyle manager Derek Adams.