The 34-year-old off-spinner took 10-115 in the second Test at Edgbaston concluded Sunday - extending his world record of ten or more wicket hauls in Test matches to 15.
But, set just 78 for victory, England won - with a day to spare - by six wickets, despite Murali's second innings haul of four for 29, to go 1-0 up in the three-match series after the first Test at Lord's was drawn.
Murali, who has played for English counties Kent and Lancashire, will be nearing 40 by the time of Sri Lanka's next tour of England in 2011 and he made it clear Tuesday he thought the Trent Bridge fixture would be his last Test on English soil.
"I am very determined to win at Nottingham and go out in England on a high," Murali said on Tuesday.
"I would love to draw the series now from the position we find ourselves in. We have an important one-day series afterwards but this is the big one for me," he also wrote in his column on the Bigstarcricket.com website.
"Although we have a young team, we have seen both at Lord's and at Edgbaston that these youngsters are capable of putting in some great performances," explained Murali of matches where his side had batted gamely in the second innings.
"We just have to make sure that we all perform together as a team rather than as individuals," Murali, who said his Edgbaston return was a "wasted effort" because it was in a losing cause, added.
"In both Tests we let ourselves down in the first innings and then battled back in the second innings.
"It would be nice if we could give ourselves a chance to get into the game this time instead of keep chasing it."
One England batsman who has appeared, so far at least, to get the measure of Murali in this series is Kevin Pietersen, whose dynamic 142 won him the man-of-the-match award at Edgbaston.
Murali last played a first-class match at Trent Bridge in 2003 when Pietersen (now with Hampshire) scored 100 off 99 balls for Nottinghamshire against Kent.
Muraltharan has taken 624 wickets in 105 Tests at an average of 22.28, a tally that also includes 52 hauls of five or more wickets in an innings.
Only Australia leg-spinner Shane Warne, with 685, has taken more Test wickets than Muralitharan.
But Murali's career has been dogged by controversy over the legitimacy of his unique action, which saw him no-balled for throwing during Sri Lanka's tours of Australia in 1995/96 and 1998/99.
Two years ago his 'doosra' delivery (a ball which turns away from the right-handed batsman, the opposite of a standard off-spinner) was reported by match referee Chris Broad, the former England opening batsman.
That led to a general inquiry into throwing by the International Cricket Council (ICC) which in turn sparked a relaxation of the rules governing Test, one-day and first-class matches after it was found that many bowlers were bending their arms in delivery, contrary to the Laws of Cricket.
Most hauls of 10 or more wickets in a Test match (player, country, number of times taken 10 or more wickets in a Test match, Tests):