Adam scored a penalty in the 76th minute, one minute after having one saved by Heurelho Gomes.
Jermain Defoe rescued a point for Spurs a minute from the end.
"It's a good result here," Adam told ESPN. "They've played in the Champions League and they've got some top international players. To be one ahead with eight minutes to go is disappointing, but the way we've come here and played, everyone should be proud of their efforts.
"Unfortunately, we never got the three points but we're still in the mix."
The draw moved Blackpool out of the relegation zone on goal difference ahead of Wigan Athletic, with two games to play, home to Bolton Wanderers and away at Manchester United.
After missing the first penalty, Adam was involved in a dispute with DJ Campbell over who would take the second.
"That just showed everyone wanted to step up to the mark," Adam said. "After missing it I felt I had to take the second. The important thing is the team and we managed to get the goal. Hopefully, we can move on to next week because we're still in the mix."
Ian Holloway, the Blackpool manager, had nothing but praise for his players.
"There's only one word for me: pride. We needed to play well and we did against a fantastic side and you can see the improvement my club has made," he said.
"We believe in ourselves again. We've had a little wobble but there's a few games to play yet."
He added: "The most important thing for me is we needed something today and we got something."
Tottenham now face a mountain to climb to make next year's Champions League after the latest big mistake by Gomes gifted Blackpool the lead at White Hart Lane.
Just a week after spilling Frank Lampard's routine 35-yard shot, the Brazilian was guilty of a gaffe that gave Blackpool the advantage with just 15 minutes left.
Moments after saving Adam's first penalty, the former PSV Eindhoven goalkeeper barged over Gary Taylor-Fletcher in the box to give the Scot his second opportunity from the spot.
Spurs seemed destined for only their second home league defeat of the season before Defoe fired home with under two minutes left. Harry Redknapp's team go to Eastlands on Tuesday with a six-point gap behind Manchester City with three matches left.
* Press Association