However, after starting so brightly against Baghdatis, Britain's number one was swiftly brushed aside and was in reflective mood after his 61-minute loss.
"I got off to a very good start and then started making mistakes. I was not really timing the ball very well and I didn't serve particularly great," Murray told the BBC.
"I struggled to adapt. It was very fast. I didn't adjust to the conditions so I may need to think about how to prepare better."
With tournaments coming up in Indian Wells and Miami in March, Murray also played down any injury concerns after enduring some pain in his left wrist.
The 23-year-old had intimated he would take a lengthy sabbatical after his extensive efforts in Australia last month, but instead opted to compete in the Netherlands in a tournament he won two years ago.
Despite his lack of preparation, he began his first-round encounter against the unseeded but lively Baghdatis in sparkling fashion.
Highlights - Djokovic ends Murray's slam dream in Australian Open final
Two breaks of serve had Murray cruising at 3-0, and although the Cypriot, runner-up at the 2006 Australian Open, fought back with a break of his own, the Briton still looked favourite after steadying the ship at 4-2.
But the wheels then fell off as his 25-year-old opponent secured the first set in 39 minutes with four games on the bounce.
The first three games of the second set went with serve, only for Baghdatis, who beat Murray at Wimbledon in 2006, to turn on the style and seal a 12th game out of 14 to clinch victory and a second round spot.
Baghdatis said: "I always try to fight and find a solution to win, Andy played good at the start, I had to break the rhythm, he began making mistakes and lost concentration.
"I finished it off and I'm very happy. He could be tired from Melbourne, when I played the final in Australia, I was in bed for a week, it's tough to come back. I took my chances today, bad luck for him."
It is not the end of Murray's participation in Rotterdam this week as he and brother Jamie will be involved in the doubles after receiving a wildcard. They will face France's Julien Benneteau and Jo-Wilfried Tsonga in their opening match.
"Physically I feel OK," Murray added. "I was a bit slow and not very sharp but the doubles will help with that."
Djokovic was ruled out of the World Tennis Tournament because of a shoulder injury and is still needing another week's rest before playing again.
The new Australian Open champion was replaced as top seed by Swede Robin Soderling, who began his defence of the Dutch title with an easy win in less than hour over local favourite Robin Haase.
Two second round results on Wednesday included a defeat for fifth-ranked Jurgen Melzer by unseeded Croat Marin Cilic, while Jo-Wilfried Tsonga had to work hard to beat France's Michael Llodra 4-6 6-4 6-2.
Victory for the eighth seeded Tsonga, who lost the 2008 Australian Open final to Djokovic, came a day after he declared the era of domination by Roger Federer and Rafael Nadal over.
"Federer and Nadal are not alone at the top of the rankings any more," said Tsonga. "Maybe on clay, Nadal's victories are still the same, but not on other surfaces.
"Djokovic and Murray are beating Nadal and Federer very often, all the players are improving their games. It's not just about Nadal and Federer any more."
Other first-round results: Feliciano Lopez (Spa) bt Florian Mayer (Ger) 6-3 6-4 Mikhail Youzhny (Rus) bt Marcel Granollers (Spa) 6-2 7-6 (8-6) Benoit Paire (Fra) bt Gilles Simon (Fra) 6-2 2-6 6-3 Marin Cilic (Cro) bt Mischa Zverev (Ger) 6-2 6-4 Michael Llodra (Fra) bt Nikolay Davydenko (Rus) 6-3 7-6 (7-4) Viktor Troicki (Ser) bt Thomas Schoorel (Ned) 6-2 7-6 (7-1) Dmitry Tursunov (Rus) bt Andrey Golubev (Kaz) 6-4 7-5 Jurgen Melzer (Aut) bt Jesse Huta Galung (Ned) 6-4 6-4 Jo-Wilfried Tsonga (Fra) bt Grigor Dimitro (Bul) 6-4 6-4 Tomas Berdych (Cze) bt Guillermo Garcia-Lopez (Spa) 6-1 6-2 Thiemo de Bakker (Ned) bt Philipp Petzschner (Ger) 6-4 0-6 6-1 Jarkko Nieminen (Fin) bt 3-David Ferrer (Spa) 6-3 6-4 Philipp Kohlschreiber (Ger) beat Lu Yen-Hsun (Tai) 6-4 7-6 (7-5) Robin Soderling (Swe) bt Robin Haase (Ned) 6-3 6-2 Ivan Ljubicic (Cro) beat Sergiy Stakhovsky (Ukr) 7-6 (7-3) 6-3
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.