Liverpool fell foul to Basel in the final group match of phase one, and it was a defeat that Heskey believes the Reds should push out of their minds by virtue of a good run in the UEFA Cup.
He said: "The Champions League is the best competition and it's where we all want to play. It didn't happen for us this season and we were all bitterly disappointed to go out in the first round.
"But now we want to show the rest of Europe that we are a good side and that we were just a bit unlucky not to stay in the Champions League.
"Obviously the UEFA Cup isn't as big a competition, but it is still one we want to do win. It is important we perform well on Thursday night and hopefully establish a lead to bring back to Anfield for the second leg."