Ryan Naderi’s 82nd minute goal was the difference at Hampden as the Light Blues set-up a final with either Hearts or Hibs in December.
While pleased to progress, the manager says there are learnings for his team to take from today’s performance.
Speaking to RangersTV at full-time, McInnes said: “I am absolutely delighted, that was what we set out to do today to make sure we got the club into the final.
“We needed to try and bring a performance that would allow us to have a bit of confidence to get through but it was patchy to say the least at times.
“In the first-half it was far too ponderous and I never thought we showed enough authority in the game. We never moved the ball quick enough. The stats will tell you we had 75 per cent possession and 25 shots and it is actually really not good enough that we can only have five shots on target.
“I thought we were guilty of rushing things when we needed to show calmness and we needed to show more tempo and intensity.
“I always feel there are goals in us and I always feel a goal coming, but equally there were still too many moments where we were caught in transition by not making good decisions in their final third, by not looking after the ball that we left ourselves vulnerable to a couple of counter attacks.
"I have been involved in Rangers teams in the past where semi-finals aren't always straight forward so it is just about getting through and thankfully we have done it and we come back in December and it is important we get the job done and win it.”
With the final in mid-December, McInnes said it is important everyone keeps driving in the weeks ahead.
He said: “There are clearly improvements still to be made but it is important that we keep winning. I am delighted for my players and the supporters because I know how important it is for us to be in finals and this has got to be the norm going forward.
“It doesn't do us any harm to have that in the bank something to look forward to, it keeps the feel good factor amongst the supporters and the club.
“We have all got that to look forward to but for the players, and I have just said it there, it is important between now and then that if you are in your team do your best to stay in the team and bring the performances and if you are not in the team get yourself in the team and everyone has got to keep driving each other on through our league campaign.”
