"Dupy's magic at the end was as good as it gets," said Cockerill, who has been in charge at the 2001 and 2002 Heineken Cup winners since Heyneke Meyer returned to South Africa.
"It was a world class finish, that's all you can say."
Leicester currently top the Guinness Premiership after six victories in their last seven games but Cockerill admitted that his side didn't produce the perfect performance in front of a crowd of 26,100 at the Walker's Stadium.
However, the former Leicester hooker was delighted with the attitude shown by his players, especially after the disruption of losing England fly-half Toby Flood to a dead leg prior to kick off.
"We could easily have lost the game, there's no doubt about that," added Cockerill.
"It could have gone either way, but every game against Bath this year has been the same.
"We said to the guys at half-time just to keep playing and not go into our shells. Considering Toby dropped out late on and we were without Aaron, I thought our shape was quite poor at times but we kept playing and that mentality brought us through in the end.
We weren't perfect . We made some mistakes but we kept playing and we wanted to win. It wasn't enough just to be in the quarter final and be doing okay. They wanted to go to Cardiff and they got their reward. The players have to take credit for that."