Pennant's goal was the highlight of a frustrating match that dominant Stoke should have won more comfortably with Kenwyne Jones, Marc Wilson and Jonathan Walters failing to convert first-half chances.
Allardyce said: "At home I haven't seen us play that badly since we've been back in the Premier League, sadly.
"We have to accept that at this moment in time it looks like we're still establishing ourselves in the Premier League.
"We still can't quite reach the level of consistency this league demands. It was a really off day for us, a bad day. Our back four limited Stoke very well.
"But the front six in terms of creativity really wasn't there. It really wasn't good enough and we played poorly, individually and collectively."