The Dons had lost five semi-finals in the previous five seasons but McInnes has led them to a long-awaited final at the first time of asking and he stressed that his team are only responsible for what happens now.
More than three-quarters of the 16,761 capacity crowd at Tynecastle were Aberdeen fans and the players showed no signs of stage fright when Hayes fired them ahead in the third minute after Rooney had latched on to a poor goal kick from Steve Banks.
McInnes said: "Obviously we can't affect what's happened in the past, whether it's history that was good or disappointments.
"This is our team's first chance of a final together and they have done it and they deserve great credit for that, regardless of what's happened previously at Aberdeen.
"They have a fantastic work ethic and a great spirit and they have a great winning mentality. They now have a chance to lift a trophy which is a fantastic opportunity and we look forward to it.
"A lot of questions are always asked about Aberdeen teams - when the level of support that we got today and when expectation comes, that we fall short. And I think that's unfair to put that on these players.
"The players responded the right way. They have been consistent all season and have handled tough ties in the cup."
Captain Russell Anderson stressed that the way to deal with the fans' expectations was to keep a level head.
"It means an awful lot to an awful lot of people, who work at the club and support the club," the defender said.
"It's well documented that it's a long time since the club made a final but I think that's key - we have only made a final, we haven't won it yet.
"We will enjoy it tonight and I'm sure the fans will enjoy it but it's back to business on Monday to prepare for the Celtic game."
Aberdeen had to withstand some intense pressure before doubling their lead through Pawlett in a 32nd-minute counter-attack, and did not look back after Rooney scored on the break just after the hour mark.
McInnes said: "I thought we managed the game far better in the second half than the first. We got off to a fantastic start but it was almost as if St Johnstone scored, we invited so much trouble into our box, giving away needless fouls and a bit too frantic.
"The second half was far more controlled, I thought we were outstanding in the second half and played with a lot of confidence and intelligence."
St Johnstone manager Tommy Wright struggled to come to terms with the heavy nature of the defeat.
His side bombarded Aberdeen for much of the first half and Frazer Wright headed against the bar early in the second period.
"I felt we put a lot into the game and ended up with nothing," the Saints boss said. "The 4-0 scoreline is extremely harsh on the players because I thought we played extremely well.
"After the first goal we did dominate possession and put Aberdeen under a lot of pressure but just didn't have that killer ball.
"But we gave the ball away cheaply and they countered on us, and they were clinical.
"Even at 2-0 I thought we were very much in the game based on how we had played. We hit the bar and then we give away possession again and they counter on us and we are 3-0 down and there's no way back from that against a side like Aberdeen."
- Sports & Recreation
- St Johnstone
- Adam Rooney
- Peter Pawlett