Vincent Janssen scored his first Premier League goal from the penalty spot at White Hart Lane but Mauricio Pochettino's men have found goals hard to come by, with Harry Kane still recovering from an ankle injury.
Tottenham have not scored from open play now in 360 minutes and they paid the price again as Leicester's Ahmed Musa grabbed the visitors a hard-earned point.
"It's very frustrating," Dier said. "We controlled the game from start to finish and we know what Leicester are going to do.
"We know their style, so we're very disappointed because we didn't create more chances and obviously didn't score enough goals.
"We'll keep playing, keep improving the way we play, try to get better and try to start winning games because we're drawing too many."