Davids bemoans wasted corners
Cardiff boss Malky Mackay was satisfied with his team's stubborn resistance as they held Watford in a goalless draw.
Goalkeeper David Marshall was in inspired form as the Welsh visitors maintained their eight-point automatic promotion cushion with only six games remaining.
The Hornets pushed hard for the much-needed win in a pulsating finale but had to settle for the spoils leaving them three points behind second-placed Hull.
"I'm very pleased with the intelligence of my team's performance," Mackay said.
"We came away from home and kept a clean sheet against the highest scorers in the league. But for Troy Deeney's header and a good save, I thought we kept them very quiet.
"We kept a clean sheet, it's our 16th of the season, I thought we started really well, we passed it really well and in the second half they obviously had to come at us and were chasing us. They were at home, they needed to win.
"So I thought it was a real dogged and intelligent second half in terms of the way we played and stopped the spaces in behind us. You can always create chances, you can always lose goals.
"I thought (Manuel) Almunia made a fantastic save in the first half from Kim (Bo-kyung) and David Marshall made a great save from Deeney in the second half."
Mackay added: "To be challenging at the top of the league I think you need a bit of everything in this league.
"You need experience, you need energy, you need youth, you need goalscorers, you need clean sheets, you need a mixture of it all."
Scott Doe scored the only goal of the game after five minutes when he crashed a near-post header into the back of the net from Matthew Saunders' well-flighted corner kick.
Defeat for Exeter was their third in succession and all but ends any hopes of automatic promotion. They remain in seventh, but the chasing pack are closing in with just two points separating them and Bradford in eighth.
"It was disappointing," Tisdale said. "It has been a really bad week for us and I stood in the dressing room and listened to the players have their say.
"I'm pleased they said their piece. It wasn't heated, but it was frustrated and I am quite philosophical about it. I was very disappointed losing on Monday (against Rochdale) because at this stage of the season, you are fighting for points and we were leading with five minutes to go. We lost and that was a killer for us.
"We conceded an early goal and I would like to think we'd have got it back. It was a hard ask, but the play was disjointed. Our decision making was impaired by anxiety, frustration, panic and a bit of this and a bit of that.
"It was by no means a strong performance, but there was a lot of effort. We started the game with a substitution in the first minute and it was just a very disjointed day.
"I am desperate to get into the play-offs, but we are finding it very difficult at the minute. But it's not over and we go again at Rotherham on Tuesday and we will attack it in the best way we can."
Scott Doe scored the only goal of the game after five minutes when he crashed a near-post header into the back of the net from Matthew Saunders' well-flighted corner kick.
"We got our game plan spot on, which makes a change!" Burnett said. "It was an awesome display by our players and I can't praise them enough.
"It was a great start for us and it gave us something to hold on to. We didn't play brilliantly well, but the performance was brilliant and you need that in games when you are fighting for your life. We will take points any way we can.
"I know Exeter haven't been on a great run, but this is a difficult place to come and win. I know Paul Tisdale very well and I hope they do well because they play football the right way and they have some very good players.
"We are a young team and we got deeper and deeper and we showed some inexperience and naivety at times, but I thought we looked the more likely to score and we defended superbly."
Second-half strikes from Jay O'Shea and Sam Togwell mean the Bees sit two points above the relegation zone.
"If you have so many corners and you have the better of the play you should get something from the game," said player-manager Edgar Davids.
"We didn't give away too many chances in the first half and they get half a chance and they score. That's the way football is.
"We always go for the win and how we go for the win is not important but we have to go for the win.
"We played a top 10 team, we out played them and we were the better team but then you see why they are at that level because they get half a chance and they score and that is the difference.
"But when you get the chance then you have to convert it. You can play for two or three days but if you aren't sharp and you don't have the determination to score then nothing is going to happen.
"I think that when you get the chance you have to convert and if you have so many corners you should get something out of it."