Yet in extra time, Bryan Habana intercepted Ian Madigan's pass to dive over and his converted try proved enough for Toulon to hold on for a 25-20 triumph, despite Sean O'Brien's late score.
Leinster will now be looking to bounce back in the GUINNESS PRO12, where they face a tough challenge to make the semi-finals, currently lying in fifth and eight points behind fourth-placed side Ospreys.
But O'Connor insists his players can draw inspiration from their European run as they prepare for a crucial derby against Ulster at the Kingspan Stadium on Friday night.
"The overriding emotion is probably pride, really. The effort the lads put in across the course of it was fantastic and it's incredibly disappointing to come second," said O'Connor.
"It showed that we can compete against probably the best club side ever put together.
"We were probably inaccurate at key moments in the second half. I thought we dominated for large periods, put them under pressure and made that tell on the scoreboard.
"We led for large parts of it and were probably the better side for large parts of it but we came second in extra time and that determined the result.
"We'll go back to Dublin and re-group, see how the bodies are.
"We've got to get three wins in the league to get ourselves any chance and hope other results go our way. From that perspective, we'll regroup and dust ourselves off and have a look at the challenge of the next three games."
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