Rangers faced competition to sign a number of their top targets from English clubs.
The Gers had a number of players that they wanted to bring to Ibrox during the recent transfer window, but Warburton was worried that interest from other clubs would scupper his plans.
However, in the end, Warburton managed to acquire most of his prioritised recruits, with many of Rangers' new arrivals rejecting switches to English clubs in order to move to Scotland.
And he said: "We knew a lot of those players, the likes of Wes [Foderingham] we’d played against Swindon many times, [James] Tavernier with Rotherham and Bristol City, Waggy [Martyn Waghorn] I knew very well from Leicester City and Rob Kiernan we signed at Watford when he was a young boy.
“So a lot of these players we knew about. The big worry for me was could we get them before others did.
“Rob was very close to signing for a Championship team, likewise Waggy and Tavernier and they turned down offers in the Championship down south to come here.
“So that was the biggest concern I had, could we move in time to get them on board."
Rangers' new signings have added some much-needed quality to their team, and almost every addition Warburton has made has already paid off.
The Gers are blowing away all comers in the Scottish Championship at the moment, with the side having won all nine of their league matches to date.
During that time, Warburton's men have scored 31 times and only conceded five goals at the other end - making them a real force to be reckoned with.
It is form which stands in stark contrast to last season, when Rangers were well off the pace, and Warburton will feel that the club's productive summer is a major contributing factor to their positive start.