Pizzi's Valencia were 3-1 winners at the Mestalla on Thursday but cruelly bowed out of the competition following Stephane M'Bia's 94th-minute goal that saw La Liga rivals Sevilla progress on away goals after the semi-final tie finished 3-3 on aggregate.
Despite being on the cusp of their first European final since winning the UEFA Cup in 2004, Pizzi had no complaints with the efforts from his players.
"We've given everything we had and there's absolutely no reproach for anything my team has done," Pizzi told reporters post-game.
"We did what we needed to do and more. We deserved to reach the final.
"Something like this happening won't be the first time and it won't be the last. This is football."
Valencia needed to overturn a two-goal deficit after their 2-0 defeat in the opening leg.
They produced the goods early on with two goals in the opening 26 minutes courtesy of Sofiane Feghouli and a helping hand from Sevilla goalkeeper Beto, who failed to keep out Jonas' header and was credited with the own goal.
Valencia's tail was well and truly wagging with 20 minutes remaining when Jeremy Mathieu found the back of the net from close range.
But as the home side appeared seemingly poised for a spot in the final, Sevilla's Cameroonian midfielder M'Bia popped up in the fourth minute of injury time to shatter the hearts of their Spanish counterparts.
"I'm not going to take anything away from Sevilla," said Pizzi. "I think we did enough to deserve being in the final.
"Justice doesn't always participate in football. We can rest assured, we're on a road that will bring good things."
