The head of football's governing body witnessed a key fixture in the Premier League's relegation battle, while also wants to make Fifa cost efficient
The 45-year-old, who was elected as Sepp Blatter's replacement in late February, was in Wales for the 130th International Football Association Board annual general meeting, which is being hosted in Cardiff.
Among the topics to be discussed is the subject of video replays which are expected to given the green light for testing in the near future, with the president himself eager to get the ball rolling.
Yet the Fifa supremo's attention was turned to the Premier League on Saturday, with the Swans securing a 1-0 win over Norwich following Gylfi Sigurdsson's second-half strike.
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Speaking of the trip, Infantino expressed his wishes to make Fifa more cost efficient after explaining why he flew to Cardiff with budget airliner EasyJet over a private jet.
He said: "I will not start travelling by EasyJet [all the time] but I will always take the best option and everyone should know this and everyone in Fifa should be working to optimise the costs.
"This was my job in Uefa for the last seven years as general secretary. This will not be my job in Fifa anymore but I will give the philosophy from the top.
"You can ask any director in Uefa, one of my priorities has always been to try to optimise the costs as we have to be responsible about the money which is not our money but is football's money - and I'm very serious about that."
Infantino, who formerly served as Fifa's secretary general, polled 115 votes in the race for the presidency last month, 27 ahead of closest rival Sheikh Salman bin Ebrahim al-Khalifa.