Inverness CT manager John Hughes admits Dundee "did enough" to defeat his side at Dens Park and that his own team did not merit more than a point.
Inverness were dominated after the interval with Kane Hemmings eventually cancelling out Ross Draper's opener.
"We've got [Owain] Fon-Williams to thank for making three or four wonderful saves to keep us in it," Hughes told BBC Scotland.
"We were second to every ball and I'm happy to come away with a point."
Dundee recovered from Draper's strike and spent most of the second half in and around the Inverness penalty area as they controlled the game.
"You have to be honest," said Hughes. "I felt in the first half the two teams were nip and tuck, we played some nice stuff and got our goal. In the second half it was all Dundee.
"My frustration was how Dundee were getting in so easily and I'm really disappointed with the goal that we lost and how it came about. We need to defend that better.
"We were second to every ball and that gives the other team the impetus to get on it and play. We just dropped off it, especially in the second half today. It's not a skill or a technique thing, it's a mental thing."
Dundee manager Paul Hartley, meanwhile, felt that his side created enough chances in the second half to win the game comfortably, and he praised his players for remaining patient as they pushed for an equaliser, even as Hemmings, Rory Loy and Greg Stewart all missed a series of chances.
"In the first 10 minutes we didn't start that well but in the second half we were terrific," said Hartley.
"We could have won that game 5-1, we had some fantastic chances and on another day you bank on Stewart and Hemmings scoring more than that given they chances they got.
"But the team kept going and I thought we were brilliant in the second half, some of our passes and combinations.
"You've got the give the [Inverness] goalkeeper credit, he made some great saves, but we kept going, we never gave in and I've got a smashing bunch of lads.
"[The battle to finish in the top six] is exciting, there's not a lot between the clubs. We've got a big week coming up, a real testing week for the club, the players and myself, and it's a week we want to do well in."