Blues boss Jose Mourinho signed Costa and Cesc Fabregas in the summer for around £60m - but Azpilicueta claims it is down to more than new signings.
He said: "I think we are stronger mentally now.
"The players who came have given us another dimension as well.
"Last year we were so close to winning the title, and this year we know it will be tough but that's what we want. We will see in May.
"We're on top of the table but that's a long way off, but we want as few problems as possible up to then."
For the big stories and the banter follow us on Twitter: @tribalfootball