Exeter head coach Rob Baxter admitted his team lost their focus as they almost let an 18-point lead slip away in the closing 10 minutes against Wasps.
The home side looked to be cruising to their first Aviva Premiership win of the season as they led 30-12 with time running out at Sandy Park, yet a pair of converted tries meant the eventual margin was just 30-26.
Last weekend's season opener at Northampton was a setback, and Baxter was willing to accept there was an element of relief when the final whistle blew.
"We have done the important thing of banging in a win in our first home game and now we can sit back and look at the bigger picture," said Baxter. "We have had Northampton away followed by Wasps at home and collected four points; it's not a bad start.
"The important thing for us now is to push through and make sure we keep improving and collecting points. A challenge for us has been that when we are ahead to turn the screw and close out the game.
"It has been a bit of an Achilles heel for us. I wouldn't say that we stop working but we maybe lose a bit of focus and I think that is what happened today. We will obviously talk about it but the reality is that Wasps are a good side.
"I think that we did well to get the daylight that we did and then going into that final quarter, no disrespect to Wasps but with that much daylight and needing a try for a bonus point, really the ball is in your court to get the full amount from the game.
"I'm a frustrated a little by that but probably more frustrated by the manner in which we ended up in our own 22 for an extended period; conceded two relatively soft tries, considering how we defended for the rest of the game.
"You can talk at length about what you get right or wrong but sometimes (you need) to just have the character to push through to win under a little bit of pressure, which we were at times because the scores were tight at half-time."
Exeter led 16-12 at the interval.
"I think that tactically in the first 20 minutes we controlled territory and possession; our actual phase play improved and we started to get some tempo into the game, but then to concede two tries is tough. But we have won," Baxter added.
Tom James crossed for the only try of the first half, his first since joining the Chiefs from Cardiff Blues.
Fly-half Gareth Steenson added the conversion and three penalties while fly-half Andy Goode replied with four for Wasps.
Exeter scored two further tries in the second half through flanker James Scaysbrook and a second from James, converted by Steenson. But Wasps kept battling with tries from wing Christian Wade and flanker Ashley Johnson both converted by Goode.
Baxter added: "Tom [James] is looking good and I think the best thing about him is that the more he settles in, the more he will do. I think we are only scratching the surface with Tom, I think there is a lot more of a footballer than people are aware.
Wasps director of rugby Dai Young praised his bench players who came on to salvage the visitors' second losing bonus point in as many games.
He said: "We are still a young pack and I thought we had the edge in the scrum as well as challenging them in the line-out. We were very wary of their contact area but we controlled that as well so I was quite pleased with that.
"In fairness to Exeter I thought they had real bite in their defence, we struggled to get any real penetration, we tended to be quite lateral in our attack, we struggled to break them down and when they had opportunities they took them.
"We are a little disappointed with one or two of the tackles we fell off but in fairness you have to put your hand up sometimes and say that on occasions their attack stretched us so we are a little disappointed in some of the points we gave away.
"We have had two bonus-point losses, at one stage today even the bonus-point loss looked unlikely, but we came back to sneak a bonus point at the end."