West Indies beat England by four wickets in the first Test to take a 1-0 lead on the three-match series.
Broad made his feelings known on national TV after failing to make the cut and Hussain stated he was right in doing so.
West Indies batsman Kraigg Brathwaite played a knock of 65 runs in the first innings while the team was bowled out for 318.
The toss took place in the second session of the opening day after the first session was washed out due to rain.
The covers were on the field at the Rose Bowl in Southampton when the toss was due to be made at 10.30 a.m. local time.