Wolves began this season poorly, losing seven and drawing one of their first eight league games.
A run of four games unbeaten, including successive wins over Southampton and Fulham, suggested a corner had been turned.
But they were beaten by Bournemouth and then lost heavily to Everton before defeats by the Hammers and Ipswich.
They have also struggled defensively, having conceded a league-high 40 goals and let in two or more goals in 13 of their 16 matches.
On Saturday, they went behind through a Matt Doherty own goal and although Matheus Cunha hit back, they were undone by Jack Taylor’s 93rd-minute header.
In addition, the Molineux club has struggled with off-field issues, with Mario Lemina being stripped of the captaincy after an altercation with West Ham United’s Jarrod Bowen on Monday.
On Saturday, Rayan Ait-Nouri was sent off in the tunnel for a second yellow card after clashing with Wes Burns, while Cunha fought with Ipswich’s security, barging into one before ripping his glasses off his face, as well as striker Liam Delap.
In the wake of the defeat, O’Neil said he had “never had such a struggle” to coach a group of players.
Prior to Wolves, he had a year-long spell at Bournemouth in the 2022-23 season, helping the south coast club avoid relegation before being sacked and replaced by Andoni Iraola.