James Anderson and Muttiah Muralitharan had nine balls to snatch one wicket for victory after the hosts finished nine down chasing a massive 366.
Lancashire's failure to bowl Durham out in 101 overs on the final day of the County championship heightened their inability to finish sides off.
But Watkinson said: "426 runs were scored in 101 overs by sides just playing normal cricket on Friday.
"I don't think there was any chance of us declaring early to set them 320 or 330 with a full day's play and maybe a 30 or 40 run start in the evening.
"We got our second innings runs at four an over, and I'm quite surprised at people raising the declaration as an issue."
Muralitharan took 3-45 in from 32 overs, while Anderson bowled superbly for his 2-46 off 26 overs.
Durham's Paul Wiseman repelled Lancashire with a match saving seven off 92 balls.
Dominic Cork also grabbed two wickets, while Glen Chapple and Tom Smith picked up one each.
"Jimmy, in particular, bowled very well," said Watkinson. "He looked a threat, passing the bat on a number of occasions. He can take a lot out of the game.
"In the first innings I thought his body language was poor - and he didn `t bowl as consistently as we know he can do.
"He saw an England selector at the ground, so went away feeling bad about the day.
"But he got himself together for the second innings, bowling a whole lot better."
Lancashire took 11 points for their fifth draw of the season and are now 27 points behind leaders Yorkshire, who also drew against Kent.
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When you have got murali, you have got to set 'enticing' targets to make sides think they can get the runs. Even give the chasing side some runs to let them think the target is gettable. Sadly Chilton and Watkinson, and hegg before, are not daring enough. Shane Warne was right. Sadly looks like Lancs are blowing this season again too