The result ensured Chelsea booked their place in the final in the Amsterdam Arena on May 15, facing Portuguese side Benfica.
It means the Blues will compete in their second European final in as many seasons following their 2012 Champions League triumph against Bayern Munich.
Cahill was a part of that winning team and said he was excited to be in another major final with the Blues.
“It's fantastic,” he said. “The first [final] went well, so we're hoping the second one goes the same way.
“Confidence is high. We have some massive games coming up. We played well and it was a positive result [against Basel]."
This week has also seen Chelsea legend Jose Mourinho linked with a move back to Stamford Bridge to take over the managerial reins interim manager from Rafa Benitez next season.
Following Real Madrid’s defeat to Borussia Dortumnd in the Champions League semifinals on Tuesday evening, Mourinho said he wanted to go where “I am loved”.
It’s led to many speculating that place is Chelsea and Cahill said he would welcome the “Special One” returning to West London.
“The lads speak very highly of him,” Cahill explained when asked what he thought of the Mourinho rumors.
“I haven’t had the opportunity to work under him, but if that was the case, then obviously from his CV and what the lads say, he’s a fantastic manager.”