Substitute Junior Hoilett had the best opportunity of the match with a 20-yard chip over Robert Green in a one-on-one with the goalkeeper which dropped onto the top of the net in the 77th minute. There were very few half-chances created by either side but Rovers had the majority of penalty-area action.
"It should have been more than a point on reflection of the opportunities that we had," said Allardyce. "We have been a little shy in front of goal all season in terms of chances created and not converted so when we got some half-chances we wanted to convert them if we could."
He added: "In the first half I think Chris Samba's shot was going in and it just touches Julian Faubert's head and goes over the bar. When things are going for you those sort of chances go in and at the moment they are not.
"When it did come with Junior he didn't quite get it down under the bar but it was a terrific show of technique and quality. Those are the small differences that make all the difference in the Premier League - it is all about inches and at the moment we are the wrong side of those inches."
West Ham manager Gianfranco Zola was satisfied with a point after three tough games in a week, praising James Collins and captain Matthew Upson.
"The two centre-backs were vital because of the kind of play they have," said the Italian.
"I think the whole team in the first half was quite bright but I knew as the game became longer and longer the team physically-wise would drop something because of the game we played on Tuesday (the controversial Carling Cup win over Millwall).
"But once again we defended very well and that is something that is very important.
"Considering all the circumstances I am pleased with the team. It is the third game in six days so I have to admit it was quite difficult."