The winger scored a brace in last weekend's victory over Motherwell before turning her attention to cup action, as the Gers continued to build on their recent performances and raise standards with every challenge.
Speaking to RangersTV after the match, Hay said: “I think it was an all-round good team performance.
“We showed on the pitch a lot of what we've been working on at training throughout the week, so that was pleasant to see.
“We pride ourselves on being a team that takes the initiative in our performances, always looking to be on the front foot rather than being reactive.
“But we still had to work hard as Thistle are a hard team to break down and hard to play against.
“I’m obviously delighted that we came here to get in the next round and that's what we've done.”
While the collective performance was pleasing, Hay was also keen to highlight the contributions of goalscorers May Cruft and Katie Wilkinson, whose efforts ensured Rangers progressed to the last four.
Wilkinson marked the occasion by reaching 100 competitive goals for the club, while Cruft continued to demonstrate her importance to the side with another valuable contribution.
Hay continued: “May's a vital player in our team; I think you can see it in her performances.
“She's got a lot of control in her game, so for her to get on the scoresheet today, I think she's buzzing and we're buzzing for her.
“Katie's such an important player for our team and it's an unbelievable achievement. I don't know many that can do that, to be honest.
“Everybody who knows me knows how much I love playing for this club and to get 200 appearances, it's special.
“I'm glad that my family were here today as well and we talked it all through, I wanted to get into the next round of the cup and that’s the most important thing I'll take away from today.”
With fixtures continuing to come thick and fast, attention now turns back to league action as Rangers prepare to welcome Hearts to Broadwood next weekend.
Hay knows it will present another challenge for the Light Blues, but believes a full week of preparation will ensure the team are ready.
She added: “I think we've had a lot of control in recent games and we're scoring a lot of goals, but we know it's a totally different test we're going to come up against next week.
“We've got a full week of training to prepare and make sure that we do the right things. I'm sure come next week; the team will be ready for it.”
