Saints had much the better of the game, but were defeated by a wonder-strike from their former Academy product on a sunny day in north London.
And their manager was left exasperated at full time after seeing his side slip down to 14th in the Barclays Premier League standings having taken just two points from their last four games.
"I think this is a cruel defeat because I think we did enough – not just to draw, but to win the game," insisted Pochettino.
"We were lacking that little of bit of luck that you need in football to succeed. We haven't had that recently and we didn't have it again today.
"I am very angry about the goal because I think we played a very good game and because I don't think we deserved to lose today."
Saints had a number of good chances, most notably through right-back Nathaniel Clyne then with a Rickie Lambert free-kick that was tipped onto the post by Spurs goalkeeper Hugo Lloris.
Pochettino's side has now failed to score in the last three games, while Spurs were restricted to half-chances – but Bale made the most of his late opportunity.
"In football you need to deserve to win but you also need to score the goals," reasoned the manager. "Today we competed really well but weren't able to get the goals that we needed to win.
"When a team has a player of his (Bale's) characteristics they can do those things that light up moments in the game and there is nothing you can do about that."
With Wigan and Aston Villa both picking up wins today, the points totals separating the bottom ten sides has closed somewhat.
11th-placed Stoke face 17th-placed Sunderland on Monday night, with Saints travelling to the Stadium of Light next weekend before hosting the Potters on the final day of the season.
And Pochettino says his side will be able to win both of those games if they perform as they did at White Hart Lane today.
"We need to make sure we get the maximum points from the last two games," he affirmed. "Today we tried to do that with everything we had, but we weren't able to do it.
"By performing the way that we have today I don't think we will be in that [relegation] battle.
"We need to work hard and if we continue to compete as today then we won't be in any trouble."