By ESPNSTAR.com staff
Bayern opened the scoring in the Group F encounter at the Allianz Arena in the 36th minute thanks to Bastian Schweinsteiger, before midfield counterpart Toni Kroos doubled their lead in the 76th minute.
Los Che pulled one back through substitute Nelson Haedo Valdez in injury-time but it was a case of too little too late, as Pellegrino was left to lament his side's slow start to the match.
"We gave the ball away a lot, especially in the first half," he said on UEFA.com. "We had no support when we brought the ball out, and we were not in the right positions.
"In the second half we improved, but against a team like Bayern mistakes like these make things very difficult."
Despite missing a number of key players through injury, the Argentine tactician refused to use that as an excuse for Wednesday's defeat.
"We pressed them [Bayern] better after the break and we know we can improve," Pellegrino added.
"We have some important players injured but that is no excuse. We had chances to draw level when it was 1-0, but the second goal was crucial.
"The players have shown good character in a difficult game against a great team. Anything can happen in the group stage and the other result tonight [Wednesday] leave things very open."
Valencia return to action in La Liga on Sunday when they visit Real Mallorca.