The Dane's side were undone by a brilliant opportunist free kick from Joe Bryan that beat goalkeeper David Raya at the end of the first period of extra time before the full-back added a second in the 117th minute as Fulham gained immediate promotion.
"Of course, it's tough to take. I think we've had a top season in many ways. I'm extremely proud of this club, I'm extremely proud of the players, the staff," Frank told Sky Sports.
"We managed to score the most goals (80) and have the second-fewest conceded goals (38)... but in football, it's the fine margins, and the fine margins were maybe not with us in some ways this season," he added.
"Definitely not in the final - you need that in the final, in a tight, tight final, the two teams cancelled each other out, you needed that bit of brilliance from Bryan, that was the difference between two good teams."
The 46-year-old Frank refused to blame his keeper for the opening goal, despite Raya seemingly being out of position and reacting slowly to Bryan's set-piece from distance.
"I will never blame David for anything. I think he's been a fantastic keeper for us throughout the season, and I think he is one of the reasons why we had the second-best defence this season," he said, adding that he was not worried about losing any of his players to bigger clubs.
"I just know one thing - that when we start next season, we will have a very strong side out there again, and we're ready to push." (Reporting by Philip O'Connor; Editing by Ken Ferris)