Last year Chelsea collected both the FA Cup and Champions League trophies under former boss Roberto Di Matteo, and a strong run-in this time around could see them lift the Europa League and claim a spot in the top four of the Premier League.
Cahill, who returned from a knee injury in Sunday's 2-0 win over Swansea, admits there are some tough fixtures ahead but wants another impressive end to the season.
"Last season was a strong finish and I hope we can do the same this year," he told the club's official website.
"We know what we have to do between now and the end of the season and we have to start by putting in performances like we did against Swansea and getting the wins.
"We're in a good position but it's dangerous because we've got some great teams coming up in Spurs, Manchester United and Everton, who people tend to forget about but they're not far away.
"Obviously we've got the cup as well so it needs a big push from the players over an important few games."
Cahill was forced to sit out the business end of last season through injury but has been recalled by interim manager Rafael Benitez, knowing the whole team have to perform to reach their goals.
"It's what the lads have come to expect at this club," he said.
"It's nothing different to what we're used to and the demands that are on us. It is in our hands, it will be difficult because we're up against some good teams but we're in a good position at this moment in time."
Sunday's win over Swansea, coupled with draws for fellow top-four contenders Arsenal and Tottenham, have moved Chelsea into pole position to seal third place behind champions Manchester United and their neighbours Manchester City.
They also hold the upper hand in their Europa League semi-final tie with Basle after winning the first leg 2-1 in Switzerland last week.