The temperamental Connolly summed up the mood when he had a stand-up row with team-mate Marlon Harewood after the Irishman had shot instead of passing.
"It shows how far we have come that we are frustrated with only drawing at Burnley. I couldn't fault the team for effort but we were let down by a lack of quality, which was unusual," said Pardew.
At least Ipswich's defeat at Stoke allowed West Ham to leapfrog above them into fifth place.
West Ham will again be without Steve Lomas when they face Walsall on Saturday. The Northern Ireland international has missed nearly a year with a series of injuries and his comeback has been further delayed by a calf strain.
