Poyet, a former Uruguay, Chelsea and Tottenham Hotspur midfielder, replaced Spaniard Gregorio Manzano ahead of the season to build on the club's third-placed finish last term.
He stepped down last week, however, following their 11th defeat in 23 matches in this campaign.
"Manzano contributed a lot and I hoped he would stay. We communicated at the end of last season but couldn't accept his conditions," Wu told Shanghai TV.
"We were also looking for alternatives while we were talking to him and, due to the short period of time, we eventually chose Poyet, but he was only our third or fourth choice."
Shenhua hoped to build on a strong finish in last year's CSL but, having missed out on the Asian Champions League group stage after losing to Brisbane Roar in the preliminary rounds, they have struggled in the domestic league and stand in 11th place.
Wu said Shenhua waited too long to replace Poyet, whose coaching career included an 18-month spell at then Premier League side Sunderland.
"We changed Poyet too late," he said. "The bad results at an early stage influenced Poyet and raised questions. I hoped he would handle it and not get distracted, but his stress increased and he couldn't hang in there anymore."
Wu also said the club had a problem with the "foreign players' selection process".
Their Argentina striker Carlos Tevez has failed to live up to expectations after a season dogged by fitness issues.
Tevez, who joined from Boca Juniors last December, is the highest paid player in the world, according to media reports when he signed which said he would earn about $750,000 (555,926.17 pounds) per week.
Yet the 33-year-old former Juventus and Manchester United striker, who cost a reported $87 million, has played only 13 games and scored three goals for Shenhua.
"As for the foreign players, we wanted to sign a big name and a good individual, and we thought Tevez was the one," Wu said.
(Editing by Toby Davis)
Share
