Neil Lennon's men made the last 16 of the tournament last term, beating Barcelona en route, before crashing out against Juventus.
And Ambrose, whose side retained their Scottish Premier League title and won the Scottish Cup on the domestic front, believes they can build on these achievements this time around.
Lennon has captured defenders Steven Mouyokolo, Virgil van Dijk and striker Amido Balde so far this summer.
"We set the target last year and we want to do better this year," said the Nigeria international.
"I don't think we have the squad to do that - I believe we have. I believe in what the manager has seen in them (new signings) and I believe they are good players. That is why they are here.
"We never rely on just two players. We rely on the whole team and the people on the bench.
"We can see the qualities of the players and we can do even more than what we did last year, if we put our mind to it and be determined to work harder."