Kevin Thomson admits Rangers were under pressure to deliver the points against Falkirk after Celtic threw down the gauntlet with a win over Hamilton.
Victory in the lunchtime kick-off on Saturday allowed Celtic to reduce Rangers' advantage at the summit of the Clydesdale Bank Premier League to seven points.
But the Scottish champions hit back just hours later to restore their 10-point lead and leave Falkirk rooted to the foot of the table, with Steven Davis, John Fleck and Steven Whittaker all on the scoresheet.
Thomson said: “We had to be on our guard, we knew Falkirk would come and make it difficult for us after getting a fantastic point at Parkhead so we had to play at a good tempo.
“With Celtic winning in the early kick-off we had to keep up our winning ways.”
Davis stole the show by grabbing the opener and setting up the other two goals but Thomson believes Fleck also showed why Rangers are so keen to retain his services.
A misunderstanding between the 18-year-old and his agent led to reports that the youngster had rejected a new deal but contract talks are now back on.
Thomson said: “I think he's shown in the last few weeks since he's come back into the team and had another wee chance just how much quality the boy's got.
“The pressure at a club like this is immense. It's hard for first-team boys with experience, never mind young boys coming into the team.
“So having the manager looking after him and guiding him in the right direction — taking him out and putting him in at the right times —will bring him on leaps and bounds.
“I think you can see the real John Fleck playing at the moment. He's a big asset to the club and I'm sure all the fans and the people upstairs in the club will be desperate to keep him.”
Thomson is confident Rangers will cope without fellow midfielder Pedro Mendes after his move to Sporting Lisbon was confirmed on Saturday.
He said: “We're sad to see Pedro go but he's made his decision to move and we've got a squad of players and it's down to the rest of the boys to step up to plate.
“He's been missing for the majority of the season so I don't think it will be a big factor on the team.”
Meanwhile, Jackie McNamara expects plans to join Partick Thistle in a coaching capacity to be put on hold until the end of the season.
An Achilles injury looks set to sideline defender Pedro Pele for the remainder of the season, meaning the former Celtic star is likely to remain at Falkirk and help with their survival bid.
He said: “The most important thing is the lad gets all the support he needs, because he's got a horrendous injury and I hope he gets well looked after by the club.
“As far as my situation is concerned, Ian McCall contacted Eddie May and asked about my availability because he wanted to take me there in a player-coach capacity just now.
“But after what's happened to Pele it's kind of changed a bit. I'm not sure what's happening at the moment. I'll need to speak to the manager and everyone else to see what's happening.”