Two second-half strikes from on-loan Sunderland winger Jack Diamond sealed a 2-0 success for the Wetherby Road outfit in a Yorkshire derby which the Bantams had the better of for over an hour.
Home goalkeeper Mark Oxley was required to make a trio of excellent stops to keep Harrogate on terms, but having soaked up everything their visitors had to throw at them, they then went down the other end and netted twice in quick succession.
And while there is no denying that City looked the more likely up until the 62nd minute when they fell behind, they ultimately ended up paying the price for not capitalising while they were in the ascendancy.
Adams, however, was unable to see past the fact that, in his opinion, Bradford were "better" on the day - a point he seemed determine to reiterate after the full-time whistle.
"Today, on the pitch, we were better than Harrogate Town, " the Scotsman insisted.
"Harrogate didn't deserve to win the match, nobody can say that they did because we had better opportunities over the 90 minutes.
"The first-half performance and into the second half, we were better than Harrogate. We created some really good opportunities.
"Harrogate had no shots on goal in that first half, they had three shots on goal in the whole game and got the two goals. We've dominated for large spells and haven't been able to be clinical.
"We looked very good defensively, we didn't allow Harrogate any opportunities and when they did get an opportunity we were 1-0 down after the deflection goes in .
"We had to chase the game after that, but we should have been ahead before then."
Continuing in a similar vein, Adams did break off briefly to praise Harrogate goalkeeper Oxley for his performance, though only in an attempt to back up the point he was so desperately trying to ram home about how City "controlled" proceedings.
He added: "We haven't taken the opportunities, they have. They've had three attempts on target, they've scored two goals. We've had more opportunities on target than Harrogate over the afternoon but haven't made that count.
"Their goalkeeper was outstanding, man of the match today. Three unbelievable saves which he had to right to make, but over the afternoon, we feel that we're just not getting a break.
"We've created enough opportunities to win the game. They are very good opportunities and I've got to say that their goalkeeper made some really good saves and that has kept them in the match.
"When you don't win the game and you've had so many good moments, good opportunities, you've controlled the majority of the game ,it hurts you because the opposition score out of nothing and that gives them a lift.
"We really should be winning this game with the dominance we had. When you're going toe-to-toe with the opposition and dominating the opposition and dealing with the threats they have away from home and creating good opportunities it's difficult for them [the players] because they're not getting a break. Other teams have had breaks."
Town took the lead on a wet, blustery afternoon at Wetherby Road on 62 minutes when Alex Pattison fed Diamond on the left-hand edge of the City area and his effort across the face of goal deflected off Oscar Threlkeld and into the away net.
Harrogate's flying winger then wrapped things up in the 71st minute after breaking from just inside the Bradford half and driving down the centre of the pitch before dispatching a composed low strike beyond Alex Bass.
Victory lifts the Sulphurites up three places to 11th in the League Two standings, while City drop down to 14th.