Adams was not so pleased when Vale ousted Sheffield United, the team he supported as a boy and still holds close to his heart, in round one.
But he was cock-a-hoop after a 2-0 win which described as a "magnificent team performance" against 10-man Wednesday, who had Francis Jeffers sent off in the 37th minute.
Adams said: "I didn't like knocking United out, but beating Wednesday was a different matter. Even if we play Manchester United in the next round, this is the tops for me.
"I know people will say we beat 10 men and of course that was a factor, but I thought the attitude of my players was spot-on from the start. It would have been a travesty if we had not gone through.
"The game plan was to give Wednesday as little time on the ball as possible and I thought our tactics were spot-on. Every player did their bit and it is not a time to single out any individuals."
Video evidence later confirmed Jeffers had butted and thrown a punch at Vale skipper Tommy Fraser, with the Wednesday man coming off worst as he trudged off with blood pouring from a cut forehead.
Vale had created the better chances even without their numerical advantage as John McCombe headed over and Louis Dodds saw a shot smothered by Lee Grant.
And they deservedly won the tie with two goals in three second-half minutes - starting with Kris Taylor's 30-yard thunderbolt which crashed in off the underside of the crossbar.
The left-back, currently on a short-term contract, fired in a magnificent dipping effort after collecting a corner from Fraser.
Rob Taylor then capitalised on some dozy defending to hook in the second from close range after Dodds crossed from the right byline.
Wednesday manager Brian Laws refused to comment on Jeffers' red card, or any possible repercussions, until he has studied the video in his own time.
But he said: "I won't hide from anything and when I've seen it everyone will soon know what the outcome will be.
"What I will say now is you need 11 players on the pitch to win football matches and I'm bitterly disappointed to be out of the competition.
"No disrespect to Port Vale, but we were always going to be up against it when you play for almost an hour with 10 men.
"We kept two strikers on the field to have a go in the second half and we had our best period of the match just before their first goal.
"It was a cracking goal which no-one could do much about, but then we conceded a second almost straight away after Mark Beevers dropped an absolute rick."