The Islanders were left red-faced when Pakistan chased down 302 in 57.3 overs on a fifth-day pitch to score a series-levelling win in the final Test in Sharjah last Monday.
The drawn series, after securing a nine-wicket win in the previous Test in Dubai, meant Sri Lanka remained in the lower half of the Test rankings at number six, an indicator of poor results in recent years.
Since the retirement of world bowling record holder Muttiah Muralitharan in July 2010, Sri Lanka have won just six and lost 12 of their 32 Tests.
Sri Lanka will be relieved the Bangladesh tour was given the go-ahead despite widespread political violence in the run-up to the opposition-boycotted general elections on January 5.
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The tourists have defeated Bangladesh in 13 of their 14 Tests, seven of them by an innings margin. On their previous tour in 2008-09, Sri Lanka won the first Test by 107 runs and the second by 465 runs.
But the Sri Lankan skipper refused to take victory for granted.
"Bangladesh will always be tough to beat at home. They have improved a lot in recent years. We need to play good cricket to win. We are certainly not going to take them lightly.