A 35-yard thunderbolt via Pedro Obiang opened the scoring before Heung-Min Son put the hosts on the level terms with a scorcher of his own late on.
The draw rises the Hammers to 15th, two points clear of Stoke City who occupy 18th.
Bodies on the line
Despite the 84th minute equaliser, Adrian commended his teammates' performance.
“We defended like a team, all together and very compact,” he told the club website WHUFC.com.
“We were hard to beat and we’ve played well against the top teams in recent weeks.
“Now we have to keep this level against teams who are lower in the table, show that we are ready to compete and take points from them too."
Having been on the receiving end of Spurs' attack for the majority of the game and the defence producing 14 blocks alone, West Ham manager David Moyes will be pleased with the point.
However, Spanish goalkeeper Adrian believes his side could have come away with more.
“To be fair, when you concede a late goal it feels a little bit like a defeat but it was a hard game," he added.
"We defended well, we had some good counter attacks and Pedro scored a great goal.
“It’s a good point away from home and we keep on a positive run.”
Defender gets special praise
The 31-year-old who's performances have been good enough to keep out number one goalkeeper Joe Hart, had special mention for central defender Declan Rice.
Having performed well against Tottenham in the EFL Cup earlier this year, the 18-year-old exceeded expectations again with a man-of-the-match display.
“I congratulated Declan after the game, because it was a big match in a massive stadium against a good team like Tottenham," he said.
“He did very well in defence, he did his job, so I have to congratulate him.”