But they ran out winners at Turf Moor thanks to Ade Akinbiyi's first-half goal and a fine performance from goalkeeper Brian Jensen.
The victory moved Cotterill's men up six places to 11th in the Championship and he said: "We are delighted with the clean sheet and with the three points.
"I thought Ade's goal was terrific but other than that it did look like it was our third game in six days. We didn't get out of the blocks like we would have liked to have done. We looked tired.
"It's about time our goalkeeper was man of the match because we have played against a few goalkeepers this season that have been man of the match."
Although Hull were the better team, neither side had been able to produce much quality until the 29th minute when Akinbiyi gave Burnley the lead, collecting Garreth O'Connor's cross , and turning while getting the ball out of his feet to stab back across goal and inside Bo Myhill's right-hand post.
The game improved after the break and, in stoppage time, Hull's Stuart Elliott had his shot pushed away superbly by Jensen to preserve the three points.
Peter Taylor thought his Hull side did enough to get at least a point. He said: "I was happy with the way that we played and I was quite disappointed to be 1-0 down at half-time.
"Ade scored a great goal but I thought we should have been level or leading and in the second half we created more chances but the goalkeeper was superb."
Burnley: Jensen, Duff, Lowe, Sinclair, Harley, Spicer, James O'Connor, Hyde, Garreth O'Connor, Elliott, Akinbiyi. Substitutes not used: Karbassiyoon, Noel-Williams, McCann, Dyer, Courtney.
Hull: Myhill, Lynch, Cort, Delaney, Edge, France, Woodhouse, Welsh, Elliott, Brown, Fagan. Substitutes not used: Duke, Burgess, Ellison, Barmby, Green.
Referee: P Dowd (Staffordshire)
* Brighton manager Mark McGhee is determined to go down in club history as the man who led them into their new stadium. Despite fierce opposition from local residents, Deputy Prime Minister John Prescott yesterday ruled the club's new 23,000 capacity stadium can be built on the South Downs at Falmer. The Seagulls hope to move from their 6,500-capacity temporary home at Withdean into their new home by 2008 after being without a home since the Goldstone Ground was sold in 1997.Reuse content