The result meant The Bees are without a win in their last four matches and they have slipped to 18th in League Two.
Allen told BBC Radio London: "I thought it was a slow start but Orient started very well. As the game grew, we got stronger and stronger.
"Second half we were the dominant team, but I don't think we created too much. We had to keep our concentration."
Barnet lost 5-1 at Portsmouth the previous weekend and then drew 2-2 with Morecambe.
"We've had a long week," added Allen. "We played well at Portsmouth but ran out of legs. Losing 5-1 hurts and hurts anyone with a brain.
"On Tuesday night against Morecambe we played very well and were very dominant.
"But we freshened it up here and brought some new players, with fresh legs into the squad."
Barmet manager Martin Allen says his side did not create enough chances in their 0-0 draw with Orient.