"I will have to have a long hard look at myself and what I am doing here," said the 58-year-old.
"After what I have seen in this match I am obviously doing something wrong... we were second best everywhere.
"I was bitterly disappointed by the performance and want to apologise to our fans who made the trip out here to watch this debacle," Toshack added.
"Cyprus were worthy winners and we were fortunate to be 1-0 up at the break.
"We tried to make some changes at the break but went from bad to worse. It was a shocking performance and we did not compete in any areas of the pitch.
"It was very, very disappointing to watch that."
Goalscorer James Collins also had a few words to say about the performance.
"It was a shocking performance and a lot of words were said in the dressing room and a lot of questions were asked," he said.
"Everyone knows we were nowhere good enough. A few home truths were said and it was needed.
"When it is a performance that bad, you have to look after yourself and we have to put the game behind us.
"We have to go away and think about our own performance as we've come off the pitch knowing we didn't play to our potential. We have to hold our hands up.
"I am not even thinking about my goal because we were nowhere near good enough and it was quite a shocking performance, to be honest.
"Something was not right, we seemed to be run ragged around the park and no one can put their finger on it. It is OK to say 'put it behind us' but when it's a performance as bad as that you cannot hide from it."
He continued, "It's up us to bounce back, even though I won't be there. Once you lose, you always want to get it out of your system and play straight away.
"The fans who travelled to Cyprus went home disappointed and we haven't done them any favours and we need to put that right. We can't perform anything like that again."