Downing is in caretaker charge of the Baggies following the dismissal of Steve Clarke earlier this month - and picked up another point in London, having overseen a 1-1 draw with Hull City at The Hawthorns in his first game.
Downing is trying to keep his players focused on the football - and is preparing them for the clash with West Ham at Upton Park on Saturday.
The Albion coach was pleased to secure a point from Boxing Day's White Hart Lane encounter, hailing the players' response to falling behind on 36 minutes to Christian Eriksen's stunning free-kick.
The Baggies were back on level terms two minutes after the opening goal thanks to Jonas Olsson, who stabbed home from close range.
And Downing, who made seven changes to his starting line-up due to the hectic nature of the coming week, says he is focusing on on-the-pitch matters, rather than those off it.
He told Sky Sports: "I've kept out of it and let the powers that be get on with their selection process. We've concentrated on the football for the last seven days and the players have responded really positively.
"I'm pleased for them as they've knuckled down and have got something to prove - and are trying to get back up the table."
Downing is hoping the Albion hierarchy appoint Clarke's successor sooner rather than later, with former Real Betis manager Pepe Mel understood to be the front runner for the hot-seat.
"I hope (an appointment) is close for the players' sake," said Downing. "I know there's a lot of speculation but I have really tried to concentrate (on the game).
"As far as I know (I will be in charge for Saturday). I'm down (in London). We have planned for the next two or three days. We are ready to go and if anybody steps in then I will gladly support whoever comes in.
"I spoke to (director of football) Richard Garlick but the interview process is ongoing."
On the Boxing Day game itself, Downing said: "The state we're in at the moment - managerless and in the bottom half of the Premier League - this has got to be seen as a bonus point.
"I thought we deserved it as we defended pretty well. We had to dig in at the back end of the second half - but in the first half we created some good chances and I thought we were unfortunate to come in at half-time on level terms.
"We've got a really busy week coming up and the game against West Ham is only 48 hours away.
"I've got a talented bunch of players in the squad - with 22 down here today - so I've got to utilise them, and it'll be an opportunity for whoever comes in to have a look at them as well."
Downing felt the decision to award Spurs a free-kick from which Eriksen scored was harsh, with James Morrison adjudged to have fouled Kyle Walker.
"I thought it was a bit harsh on Morrison," he added. "But all credit to Eriksen, it was a fantastic finish.
"I was really pleased with how we responded, though, and it was a great equaliser for us in such a short space of time. We've had a few harsh decisions of late but the players have got on with it and responded positively."