The American said Bournemouth can go toe-to-toe with every side in the league and they never feel they are out of a game, even if they go behind.
On Sunday against Manchester City, they went a goal down after 17 minutes, but they drew themselves back level through an Adams goal from a corner.
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While Erling Haaland scored his second goal of the game to restore the hosts’ lead, the Cherries were able to stay in the game in the remainder of the first half, and ensured they trailed by just one at the interval.
The Cherries went on to lose the game 3-1 – but Adams said the first half performance was indicative of their growth as a group under Andoni Iraola.
“I think that shows the character of our team for sure,” he told the Daily Echo.
“I think we've shown a lot of growth the past few seasons as well, where I think sometimes we let games get out of hand where we didn't need to.
Adams scored his first goal for the club against City (Image: Martin Rickett/PA Wire)
“Now I think we've showed an ambition to stay in every single game and stay competitive, which I think has been really, really important for the growth of our team and the character of our team.
“That's kind of what we're built off of, is high energy, high pressing, bringing the front foot on every single occasion to the opponent. And again, I think we showed good moments of that.”
Adams said the squad now firmly believes it can get results against any team – even those that are among the best teams in the league and in the world.
Asked if the Cherries had to hold their hands up and say the brilliance of City, and world-class striker Haaland, was the difference, Adams said: “Not at all.
Marcus Tavernier and Tyler Adams (Image: Richard Crease)
“You have the opportunity to play against such world class players. There's nothing better than being able to say you come here and get a clean sheet.
“And that's the mentality that we need to have every single game. He's an unbelievable player, world class, one of the best in his position.
“That being said, it's not easy because you have little lapses against a top team like that and they punish you.
“You give away a few chances. Normally it's a few goals, but again, our mentality just needs to be that we can go toe to toe with these guys.”