Bale signed a six-year contract with Real Madrid on Monday morning after finally completing his 100million euro (£85.3million) transfer to the Bernabeu.
While haggling Madrid for the best possible fee for Bale, Spurs chairman Daniel Levy also embarked on a spending spree that has seen the club bring in seven players at a cost of over £100million.
Five of those new additions turned out for Tottenham in the north London derby on Sunday, but they failed to impress as Andre Villas-Boas' team lost 1-0 to bitter rivals Arsenal.
Rose is sure that once the new signings like Roberto Soldado, Etienne Capoue and Erik Lamela get settled in, Tottenham will be a force to be reckoned with, however.
"I've been here six years now and it is a little bit surreal seeing Spurs spending that sort of money, but it's good that the chairman sees that we're not far away from breaking into the top four," the Tottenham defender said.
"We just need to push on to that next level and he (Levy) is allowing the manager to build his squad, and it's great.
"You look through the whole team and you see that we've probably got two strong players in each position - we've got a great squad this season. It's a bit sad to see the faces go who have left, but we're looking to push on now.
"Soldado's come in and he's scored four in his first three games. Etienne's come in and he's looked very solid, so I'd say those two have come in and they've not looked out of place.
"With the £30m signing of Lamela, I hope people don't expect too much from him too soon, and that they allow him to settle in and adapt, and we'll all make him feel welcome.
"We've started well and we've got Norwich when we get back from the international break, and it will be a game that we're all looking to win to get our season firing again."
Bale's departure from Tottenham was an acrimonious one despite the best intentions of the player and club.
The Welshman skipped training last week in order to try to push through his move to Madrid.
Yet despite this, Bale heads to the Bernabeu with the blessing of his team-mates, according to Rose.
"There are moments where Gareth would have just unlocked the game a lot earlier than when we've scored, and against Arsenal he would have enjoyed being out there. But I don't think anyone can hold a grudge against him leaving," Rose said.
"Me especially, I wish him all the best and I hope he enjoys the occasion at Madrid.
"I'm thoroughly excited for him, I wish him the very best and I hope he can get me some tickets for El Clasico!"