Agents of Shield tried to be connected in its first season, obviously Coulson's miraculous survival and the appearance of Jackson's Nick Fury were big pieces and they had some smaller ones ( apart from the connection to the events in Winter Soldier) but onwards from season 2 they were basically detached for the most part and then stopped entirely referencing the MCU when it became apparent that the movie franchise wasn't interested in a collaboration and the MCU never even mentioned them in a single sentence.
Jamie Alexander had made her second appearance as Lady Sif during the show's Season 2. The helicarrier featured in "Age of Ultron" was discovered by Coulson and his team in late Season 2. Gideon Malick, who was first seen in "The Avengers", was one of the major antagonists during the show's third season. The Sokovia Accords were not only mentioned during Season Four, both the Daisy Johnson and Elena Rodriguez characters were forced to sign it. Also, Team Cap's fugitive status was also mentioned during that season. The S.H.I.E.L.D. agents' encounters with a group of aliens led them and Glenn Talbot to discover that Thanos was on his way to Earth. In fact, this situation led to the events of the show's late Season 5 episodes. The whole situation regarding Project Insight played a major role in the show's mid-Season 7 episodes. And one of Gideon Malick's sons became a major antagonist. Season 6 was the only season that did not reference anything from the movies. It didn't mention the Snap. And it didn't mention the Blip because the series ended three or four years on the timeline before it happened.
Aside from Season 6, "Agents of S.H.I.E.L.D." had referenced the movies a lot during its seven-season run. At one point, during late Season 3, Chloe Bennet was complaining about how the movies never referenced the show. Which is I have found myself wondering where this claim that "S.H.I.E.L.D." had barely referenced the movies after its first season came from.