Spurs only trailed by one goal heading into the half-time break, but four second-half strikes - including a double from Radamel Falcao - fired the hosts to victory at the Stade Louis II.
"Obviously, we're a bit disappointed," Villas-Boas told the club's official website. "The first half was played at a slow tempo and both teams only had one chance at goal.
"We had a good meeting at half time but the problem was we conceded two goals straight away. We wanted to avoid that because the lads left the dressing room with the spirit that we could turn the game around and win it.
"We had belief that we could have got a better result but we'll now work hard to improve before the season starts. We were missing a number of players and we're aware that we are better than this result, but we'll take our lessons from it."
Spurs face Espanyol in their next pre-season friendly on Saturday.