Mjällby sold Stroud, 24, to Hull City on a four-year deal in early August, and the left-back made his Premier League debut in a 2-0 win over Manchester United on the opening weekend, having also featured for Sweden at this summer's World Cup.
He has made a strong start on Humberside while his former club has struggled. The reigning Allsvenskan champions have slipped to 12th in the table, only three points above Degerfors IF in the relegation play-off spot.
Karl Marius Aksum, the coach who led Mjällby to their title and a domestic cup double, has now been sacked and replaced by Andreas Brännström, a decision Stroud did not see coming.
He told Fotbollskanalen: "I was very shocked. I don't think anyone in or around the club expected it.
"At the same time, football is a results-driven business, and if you don't get the results, some change has to happen. Usually it's the head coach who has to take responsibility. Unfortunately, that's how it is."
Stroud, capped five times by Sweden, said watching his old club struggle from afar was difficult.
"It's tough, of course. It's not a situation any club would want to be in. It stings to see the setbacks there when you've left, but I know what fantastic people there are at the club, and the quality of the players in the squad."
Despite Mjällby's precarious position, Stroud remains confident they will turn things around.
"I'm not worried, it's just about getting it to click, and I believe they will."