The Blues earned the win against the dangerous Ukrainian outfit with a header from Victor Moses in stoppage time.
Cahill admitted that Shakhtar were impressive but believes that the Blues deserved to snatch all three points.
He told Sky Sports News: "Shakhtar Donetsk were very good, and at times it looked like they played five up front.
"They pushed people forward but I thought we played well. They are a fantastic team but we pushed forward at end and we're very pleased with the three points.
"They were a quality team but it was great impact from Vic with his head. We stressed this week how big a win tonight would be and it's fantastic we got over the line in the last minute."
A crucial win moves Roberto Di Matteo's side level with Shakhtar and a single point ahead of Juventus in the battle to reach the Champions League knockout stages.