The former Manchester United and Manchester City midfielder made the comment while analysing Spurs’ first goal of the Premier League encounter at White Hart Lane.
Danny Rose halved the deficit for hosts Tottenham in the 81st minute when he found the target from outside the Hammers' penalty box.
It was actually a mis-hit from the 24-year-old full-back which West Ham goalkeeper Adrian failed to keep out, and Hargreaves believes that the 28-year-old Spaniard should have stopped it from going in.
“I think he just had a bit of a brain freeze,” the 34-year-old former England international told BT Sport.
“I just think it (the ball) just bobbles and Danny Rose gets very, very lucky…. It is a weird reaction. If he had stood still, then he would have been able to catch it.”
While Adrian has been one of the better players for West Ham so far this season, his mistake did prove to be costly for the Hammers.
Rose’s goal increased Tottenham’s confidence and allowed them to get back into the game, which looked to be over for the hosts after 62 minutes when Sam Allardyce’s side went 2-0 up.
England Under-21 international striker Harry Kane scored the equaliser in injury time to take his tally to 24 goals in all competitions this season.
The youngster saw his 96th-minute penalty saved by Adrian, but he was the quickest to react and tucked in the rebound.
The 2-2 draw means that West Ham are currently eighth in the Premier League table with 39 points from 26 matches, eight points behind fourth-placed Manchester United.