A 4-2 defeat in the first leg in Gelsenkirchen left the Royal Blues with a mammoth task in the Basque region of Spain, but they gave it their best shot and, according to Heldt, earned plenty of respect for their performance.
"We gave everything and played a great game," he said on his club's website.
"We had the chance to make it 3-2 with Lewis Holtby and maybe then we would have got a fourth goal, but we leave Europe in honourable fashion.
"We wanted a bit too much in the first leg and that was our downfall."
Schalke now have no real chance of winning silverware this season, but Heldt says his side have a lot of positives to look back on.
"We played a good competition and teams like Manchester United and Manchester City went out of the Europa League before us," he said.
"Schalke have done a lot of good and what our team achieved was top drawer."