A second-half red card to Laurent Koscielny led to the capitulation on Tuesday as Arsenal were humbled 5-1 at the Emirates Stadium to lose 10-2 on aggregate.
Walcott had given the hosts the lead in the last-16 second leg, but goals from Robert Lewandowski, Arjen Robben and Douglas Costa were followed by an Arturo Vidal brace.
The England international said his team were hurting following their latest heavy defeat.
"We wanted to just show passion and commitment, that hasn't been there in the recent weeks to be honest, and we did," Walcott told Arsenal Player.
"We gave it our all, we went down to 10 men and it completely changed the whole pattern of the game.
"We should've been smart and just [opted for] damage limitation really. It's just a big shame.
"People will be saying that we don't care and stuff like this but obviously we do care. There's loads of players who are very hurt, completely, in the dressing room."
Arsenal get a chance to return to winning ways when they host Lincoln City in the FA Cup quarter-finals on Saturday.
Walcott said his side were ready for the last-eight clash, and to push for a top-four finish in the Premier League.
"We've got a great opportunity there and then we need to work on the league position," he said.
"I know we've got a game in hand [in the league], but it's going to show if we're ready for the fight towards the end of the season. Trust me - we are. We are, we just need to show that first half on a consistent basis."