Goran Popov was sent off in the 48th minute for spitting in the direction of Kyle Walker but has since apologised to the team and fans.
But Reid, whose side recorded four successive Premier League wins in November, insists the Baggies cannot afford to make silly mistakes if they want a return to form.
"At the start of the second half we shot ourselves in the foot and we were up against it with ten men against a team with the pace and power of Tottenham," said the 31-year-old.
"In recent weeks we've been shooting ourselves in the foot by going one and two down which makes it difficult. Yesterday, at the start of the second half, Goran's let us down with the red card.
"He's apologised and he's let us down, so what more can I say? He's got a suspension now and we've got Ridgey [Liam Ridgewell] to come in and fill that gap.
"I can't stress how difficult it is when you go down to ten men. It's just a moment of madness and it happens in football - but as I say we can't keep shooting ourselves in the foot like that.
"We need to give ourselves a better opportunity to stay in the game."
Reid added: "I don't think we need to dwell on the defeat, it's disappointing, but there are plenty of positives from the game, especially first half, and we've shown glimpses of the early season form."