Leicester director of rugby Richard Cockerill admitted his side had been given an "almighty fright" by newly-promoted Exeter as three late tries saw the Aviva Premiership champions recover from 11 points down to prevail 37-27 at Welford Road.

The Chiefs, despite their opening-day win over Gloucester, had been given little hope of claiming a win against a Tigers side who have lost just one of their last 34 home games but they played with no little guile in attack and plenty of bravery in defence.

They had led 27-16 with 16 minutes to play courtesy of two well-crafted tries for centre Phil Dollman and a score from wing Mark Foster, plus 12 points from the boot of fly-half Gareth Steenson. But Leicester, who had claimed the first try of the game through captain Geordan Murphy, responded with scores from wing Scott Hamilton, centre Dan Hipkiss and a late penalty try to eventually seal a bonus-point win and cruelly deny Exeter anything from a breathless game they had made a huge contribution too.

Cockerill said: "I didn't know what to expect [from Exeter] but I do now and so does the rest of the Premiership. You have to give them a huge amount of credit; they gave us an almighty fright. We could talk about how poor we were, but you have to give them credit and they are a good team who will cause a lot of problems for a lot of people. For them to come here and play like that and get nothing out of the game must be sickening, they deserved something."

While Exeter excelled, Leicester were some way below their champion best. The Tigers lineout was shambolic at times, although that was rectified somewhat by the introduction of England flanker Tom Croft at half-time, and there were several instances of poor passing and handling breaking down attacking chances.

And Cockerill admits his side have much work to do before facing Wasps next weekend. He said: "They made it very tough for us but we need to be better at certain things and up the ante. The lineout is a concern because you have field position and then you don't win the ball, or if you do it's scrappy. For me it's a repeat of pre-season and last week [against Northampton].

"You have to keep hold of the ball and build pressure, and in defence we were a little soft and were falling off tackles, but we will fix that. Everybody is happy with the five points but not the performance. But I won't walk away and say we were poor, they were bloody good."

Exeter head coach Rob Baxter agreed with Cockerill's assessment that his side merited at least a bonus point for their efforts.

"I am a bit angry we haven't come away with anything, but we did a lot of really good things, we scored three tries at Welford Road but we still haven't come away with a bonus point, which was the very least we deserved," he said. "The truth of it was we played very well for large parts of the game but the momentum got away from us in the last 20 minutes due to some poor decision-making and some little errors."

Baxter also felt his side's fearless display was down to their lack of top-flight experience. The Chiefs are embarking on their first Premiership campaign and had not played the Tigers at Welford Road since a Powergen Cup tie in 2001.

"We have no baggage in the Premiership so everything is an adventure and we have said we are going to enjoy this season," he continued. "We had never played Leicester before in a Premiership game so we were going to give it our all, and we scored some nice tries off stuff we had looked at in the week.

"But the penalty count went against us massively, especially in that last 20 minutes, and that is something we need to see if we need to work on ourselves or if we need to have a chat with the refs."