Glen Kamara’s early goal was the difference as Gers had to battle all the way to defeat the West Lothian club and set up a semi-final with Hearts.
Speaking to RangersTV, Gerrard said: “It wasn’t pretty, but I think my team have found a different way how to win, and I think we have shown this season all kinds of different sides of us.
“I thought we still had the best chances and we had some opportunities on the break where, if we found that final pass, we could maybe have scored a goal to give us some breathing space.
“But in the main, I am delighted. We came here with a plan to get into the semi-finals, and sometimes it doesn’t really matter how you do it – it is about getting over the line and that is what we have done.
Asked if this is the sort of match his side wouldn’t have won last season, Gerrard continued: “Possibly, but I think that is for other people to decide and have an opinion on. My job is to prepare the team for all kinds of different challenges, and Livingston are a big, physical team.
“You saw that again on a few occasions today, and teams with a soft-centre would fold and wouldn’t stand up to it.
“Livingston are getting more rewards than we gave them tonight and they didn’t really have a sniff.
The bright start from Gers tonight yielded Kamara’s strike, and Gerrard added: “I thought we were excellent for half an hour.
“We controlled the game, were winning first and second balls and playing at the right times – but that’s difficult to do for 90 minutes as they bombard you with long balls and they try to overload you on the second balls, but it is about sticking together when it gets tough, and I thought we did that.
“I am really pleased with the boys tonight.”
The Light Blues also lost Joe Aribo in the first-half to a head knock, and the manager updated: “I think he is okay. He has a nasty gash on his head which was stitched up. He was on the end of a bad one there, but Joe is a tough lad and I am sure he will get on with it.
“But he himself wanted to play on – that is the kid and that is the character of him. He is a tough lad and he hasn’t complained. He’s just going to get on with it.”