After moving to fourth in the table with 16 points from nine games, Chelsea visit Bournemouth this weekend before hosting Manchester United on Nov. 5.
"We move onto the next one and try to build a bit of momentum that way," England defender Cahill told the club's website (www.chelseafc.com).
"We went into the Watford game off the back of two defeats and you kind of feel the weight. It's all about character and we showed that.
"All of a sudden, when you get a few back-to-back wins you'll see how everything lifts and we'll get back to expressing ourselves as we normally do."
Batshuayi, who headed home 20 minutes from time and added his second in the dying moments against Watford, has previously struggled to impress manager Antonio Conte.
The 24-year-old, who has now scored seven goals in all competitions this season, is fighting for the lone striker's position with record signing Alvaro Morata and Cahill said the Belgian forward had responded perfectly.
"I'm sure he has things to improve but as a player that's exactly how you respond," he said.
"He's come on and changed the game for us. He scored two goals and arguably won us the game.
"I'm very pleased for him and I'm sure the manager and all the coaches are pleased for him. When you have a sticky patch, to come on and do that is the best way to respond, fantastic."
Chelsea take on Everton, who sacked manager Ronald Koeman on Monday, in a League Cup fourth round fixture on Wednesday.
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Nick Mulvenney)
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