Tottenham moved level with third-placed Chelsea thanks to an impressive victory, which came courtesy of two goals from Defoe and another from Sandro.
But the gloss was taken off the win - Tottenham's third in a row - due to hamstring injuries to Bale and captain Michael Dawson.
Dawson lasted just 15 minutes before pulling up and Bale had to come off in the second half after he stretched while shooting at goal.
Bale is expected to miss Tottenham's next two games, but Dawson could be back for next weekend's Premier League clash at Everton.
Defoe was impressed with how his team recovered from losing two of their key players, giving him hope Spurs can continue their winning streak.
"Obviously losing Gaz is a massive blow for the team," Defoe told Absolute Radio.
"Because of the way he plays you can't really replace a player like that, but at the same time I think someone else can come in.
"We're lucky because we've got some great players that can come in, play out of position, adapt and do a job for the team.
"When Gaz went off the pitch Clint Dempsey went over to the left-hand side and did well. I think we will be okay."
Saturday's derby was billed as a chance for Dimitar Berbatov to shine against his former club, but Defoe upstaged the Bulgarian with a typically ruthless second-half brace.
The England striker picked up a pass from Gylfi Sigurdsson to double Tottenham's lead after 72 minutes and a short time later he killed off the match by latching on to Dempsey's through-ball and beating Mark Schwarzer.
Defoe was overlooked by Harry Redknapp for the majority of last season, but has found a new lease of life under Andre Villas-Boas, scoring 12 goals to put him on course to beat his record of 24 goals in a campaign.
"When you're scoring goals, you're buzzing. You just can't wait for the next game because you've got that belief," Defoe said.
"You always feel like you're going to score every game you go in to, because you're scoring goals.
"You know you're going to play, you know you're going to stay on the pitch, so I just stayed focused and took the chances when they came."