The Italian giants bowed out of Europe's second-tier competition at the last 16 stage after a 2-1 home loss to Wolfsburg.
That gave the German side a comfortable 5-2 progression on aggregate and extended Inter's winless run to five matches in all competitions.
With Inter sitting eighth in the Serie A, any form of European football looks unlikely for the club next season and that is sure to increase the pressure on Mancini, who bemoaned his side's defensive errors.
"We are as disappointed as the fans," Mancini told Mediaset.
"They have every right to jeer.
"We had the chances to score more goals, but once we went behind it all became far more difficult.
"We knew that we had to score two goals and not concede, but we never seem to end a match with a clean sheet. That changes the situation.
"Unfortunately we make mistakes and therefore concede goals.
"Wolfsburg are superior to us as a team right now, but the regret is that over two legs we gave them too many gifts."
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