Jose Mourinho's side were wasteful in so-called lesser games in 2013-14, but have beaten Burnley 3-1 and Leicester 2-0 in the space of five days at the start of this term, and Cahil is thrilled with his team's start.
"They were two tough games against teams that have just come up," the 27-year-old told the club's official website.
"We slipped up last season in games which people expected us to take points from but the Premier League isn't as easy as that - you have to fight every time you take to the field.
"We've added to our squad, we know where we slipped up last year, so the first two games have been very important for us. Other teams have strengthened so it's going to be very tough.
"We know the expectation level at the club, we always expect to be in and around there [the title race] but the Premier League us very difficult."