The caretaker manager - in charge since the departure of Steve Clarke earlier this month - saw his side go a goal down to a Christian Eriksen free-kick in the 36th minute of the Premier League clash at White Hart Lane on Thursday.
But the visitors were right back in it just two minutes later when Jonas Olsson prodded home an equaliser from a set-piece at the other end.
And Downing hailed West Brom's performance against a Tottenham side who were under the permanent leadership of Tim Sherwood for the first time.
"We had good discipline and organisation and showed big hearts," he said. "We knew we had big characters in the dressing room and they showed that.
"We deserved our point and had better chances, especially in the first half.
"All in all, there were some really good performances out there.
"The free-kick for their goal was harsh but we galvanised really well and responded quickly."
And Downing reserved special praise for the club's supporters, adding: "The fans were tremendous.
"They got behind the team from the first whistle and made plenty of noise."
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