The squad returned to training after official confirmation of their reinstatement arrived on Tuesday.
"It gives you perspective of it and some time with my son and thinking about something different.
From that moment to coming home, it's been a lot of information about what may happen, what could happen," Hellberg said.
Middlesbrough enters its sixth Wembley appearance without a win in its final three regular-season games, despite finishing seven points ahead of Hull City.
"There have been a lot of emotions.
It's been a crazy time, back and forth with a lot of emotions from losing the game to being involved, trying to keep your head in the game for what may happen.
I'm very happy to be here," Hellberg said.
Middlesbrough defender Luke Ayling revealed that the squad remained largely in the dark about the behind-the-scenes legal evidence during the initial post-match uncertainty.
"We haven't trained [properly] since the last Southampton game," Hellberg added on Thursday.
The defender noted that the club's staff remained confident and urged the players to stay focused in case an opportunity arose.
"We have been in one day, but if that was our training, we would have big problems," Hellberg added on Thursday.
Ayling stated that the reality of the situation only set in when the official confirmation message came through during his family routine on Tuesday evening.
"But it was important to try and stand up for these things and try to make it possible, and everyone around the club has done absolutely brilliant," Hellberg added on Thursday.
