Exeter head coach Rob Baxter was not happy with with the way his team allowed Worcester back into the Aviva Premiership match at Sixways.
The Chiefs were flying at one stage as they led 21-3 via tries from scrum-half Dave Lewis, centre Sam Hill and fly-half Gareth Steenson, who also kicked a penalty and five conversions in the game.
However, they came within one last-second catch by wing Josh Drauniniu of blowing their 38-33 victory as the Warriors grabbed two bonus points - one for scoring four tries and another for getting within seven points of the opposition.
Baxter said: "Winning any Premiership game, especially away from home, is fantastic - but for the actual performance...
"I didn't know quite what to say to the guys (at the end) but pretty much every game we come up here to play against these has a similar ending in that it is a tight one.
"I am disappointed it ended up as tight as it was because, at times, some of our attacking play was fantastic. We were right back up there with finding space, speed of ball and speed of movement that we have had in the Premiership.
"But we coupled that with too much individual ill-discipline. It was not really a group thing but individuals keeping hands in rucks and a couple of high tackles. It swung the momentum away from us and shouldn't really have happened."
Nevertheless, the success means Exeter are a point ahead of Wasps in the race for the crucial seventh place in the league - which will give them a play-off place against a top French club for a spot in the new European Challenge Cup next season.
Baxter said: "It is going to be an exciting end to the season and Sale next week will be a massive game for us.
"Today's performance shows it is important to the players as well to be challenging for that European spot."
However, an 18th defeat this season, despite the bonus points, leaves Worcester facing the task of getting something from away matches at Bath and Saracens in the next two fixtures for any chance of survival.
The Warriors hit back to 21-15 as full-back Chris Pennell and wing David Lemi got tries and fly-half Ryan Lamb booted a penalty and conversion.
Hooker Jack Yeandle scored two tries for the Chiefs and Steenson added a penalty and conversion - but tries from hooker Augustin Creevy and Lami's second try, plus two Lamb penalties and a conversion, took Worcester to within five points of their opponents.
Had Drauniniu latched onto a Lamb cross-kick with the line at his mercy, instead of knocking the ball on in the last second, the Warriors would have won for the first time at home this season and put pressure on Newcastle above them in the drop zone.
Director of rugby Dean Ryan said: "They were sharper and more clinical than us today. They caused us problems with their wide game stressing us a bit.
"But we are not going away yet. We have got a lot of things that we can contribute and we will see what happens after each game before we start being written off by anybody.
"We have three games to survive and we didn't win today. We didn't win because we were not clinical enough about understanding roles in the first half. Today was not good enough for half-an-hour.
"We have a couple of games to go. We know it is Bath and Saracens but funny things happen and if we can get it to the last weekend, we are back at home to make a very interesting closing day."