A first-half Aberdeen goal was cancelled out by a Ryan Jack strike before Kemar Roofe found the target early in extra time at Hampden.
Speaking to RangersTV at full-time, Lundstram said: “I am really pleased to get over the line, I thought we played some really really good stuff at times but just not quite the final pass or final shot.
“We weren’t quite getting the goals that we wanted but we are really pleased to get over the line especially in the difficult conditions, I don't know why the pitch is so bad, it is ridiculous really.
“We were the better team in the first-half and we were the better team in the second-half so it was just about trying to keep going and create the openings. We had to get their goal out of our mind because we were the team in the ascendancy.”
With an Old Firm final in the diary for February 26, Lundstram is looking forward to another afternoon at Hampden with Rangers, but said the squad’s focus is fully on a big week of Scottish Premiership and Scottish Cup action this week.
He continued: “When you are at a club like Rangers finals are the games that you come to the club to play in so that is what it is all about and when you are at a club like Rangers it is all about being in the big competition finals.
“This week is massive for us again and we have got two big games. I think it'll be three games in six days so it will be a massive toll on all the lads, all the squad will have to be involved and ready to play but it is a massive week.”