Ferguson's team reached their second successive Champions League final with a 4-1 aggregate win over the Gunners, who were undone at home by a virtuoso display from Cristiano Ronaldo.
The Scotsman revealed the reasons behind his belief that that his Arsenal counterpart Arsene Wenger deserves more.
"I think we are at our strongest at the moment and Arsenal have one or two injury problems and that has been a key issue for them," Ferguson said after the game.
"We will look at Arsenal at the start of next season as one of our big threats. I know exactly how Arsene Wenger feels. When you work as hard as he has and have been there as long as he has been you deserve success.
"The problem for Arsene and myself is the longer you have been in the game the more labels you have attached to you. It is success or failure. If you win you are the greatest; if you don't you're useless.
"I don't think you have to win the European Cup to be a great manager, but unfortunately the media do."
Bye!
On which opponent he would prefer to play in Rome, Ferguson joked that he hopes to avoid both powerhouses Chelsea and Barcelona, who will clash in London on Wednesday.
"If you ask me who I want to play in the final, neither of them – I think we should have a bye!"
Tragedy
Fergie will have to do without Darren Fletcher in the final later this month, after the combative midfielder was sent off for bringing down Cesc Fabregas in the penalty area.
The United boss is convinced that the red card decision was harsh as he paid tribute to his distraught compatriot Fletcher.
"You can see the ball has moved in a different direction. It moves away from Cesc Fabregas. I think it's terribly unlucky. There is nothing you can do about it," he said.
"You saw his performance tonight and all the big games Darren is always a big player for you. He's disappointed and he should be disappointed. He's one of the most honest players in the game and to miss the final, it's a tragedy. He was distraught.
''In respect to the referee in this situation he might look at it himself without anyone asking him. We shouldn't ask him. He's competent and fair enough to look at it himself possibly. Apparently, you can't appeal and if that's the case it's disappointing for the boy.''