After a memorable victory over South Africa in 2009, Tigers welcomed the Qantas Wallabies to Welford Road on Tuesday and fought back from an early 13-0 deficit to lead their illustrious visitors going into the last 15 minutes of the match.
But a penalty and drop goal from fly-half Berrick Barnes and a late converted try saw the visitors record a 26-15 victory in front of a 20,000 crowd.
“We gave them an easy start really,” said Cockerill, Tigers' director of rugby.
“But we showed a great spirit to get back into it and we got a bit of momentum. We’re just disappointed that the momentum swayed away a bit and we did not take advantage of it.
“When we went ahead [at 15-13] we did not capitalise on that. We had an opportunity to win but did not take it.
“But the guys put in a great effort. They put their heart and soul into it.
“Australia are a good side, their set-piece was good, their physicality at the breakdown was very good.
“The scoreline flattered them a bit, but it shows if you switch off for a second a team of that quality will score. But we’ll learn from that and improve from that.
“It was a good contest, a good game, it was a great occasion for the club and the supporters, a good atmosphere, and a great experience for the guys out there.”