Barcelona Koeman was incredulous after his team lost 1-0 to Atletico Madrid in La Liga on Saturday, fiercely criticising his players for switching off at the end of the first half and allowing Yannick Carrasco to score.
"We just cannot allow ourselves to concede a goal like that," Koeman told reporters.
"The goal was our mistake, you cannot afford to lose the ball like that and concede a goal so late in the half. It's always tough to create many chances against Atletico, but when you lose the ball against them you have to do better than that."
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The Dutch coach has lost three of eight league games in charge of Barca and has been beaten by his side's two biggest rivals, having also lost 3-1 to Real Madrid.
The Catalans, who have won eight of the last 12 league titles, are 10th in the standings and nine points behind second-placed Atletico and leaders Real Sociedad.
"I'm not worried about our position in the table or the league title right now, we just need to focus on winning a series of games, that's what's most important right now," Koeman said.
"The coach is the number one person responsible for a team's results and I have to keep on believing in the players I have. But we have to improve things defensively and in attack."
Koeman also dismissed suggestions his players or the club's hierarchy could start to lose faith in him.
"Now is not the time to talk about that, we just have to work hard to improve our results," he said.
"The players did everything they could until the last second to equalise and we have to maintain that attitude in our next few games."
Koeman's problems deepened with news that Pique had sprained knee ligaments after clashing with Angel Correa while Sergi Roberto sustained a thigh injury.
Barca said Pique would undergo further tests with Spanish media reporting he could be sidelined for about six weeks.
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