On an evening that saw Jack Rodwell make his first appearance for Gus Poyet's side, Giaccherini was forced off in the first half.
Sunderland went on to claim victory at Bishop Auckland's Heritage Park through late goals from Steven Fletcher and Connor Wickham but will now await news on whether Giaccherini will be fit to feature when the Premier League season gets under way on August 16.
In front of Alan Irvine, the manager of opening-day visitors West Brom, Sunderland were made to work for victory against opponents who had also gone down by a two-goal margin against Stoke City on Wednesday.
Betis predictably named a much-changed line-up from the one who featured at the Britannia Stadium, while Sunderland handed starts to Rodwell and Santiago Vergini, the latter having rejoined the club on a season-long loan earlier in the day.
Rodwell proved an influential figure prior to his withdrawal at half-time and saw a goal ruled out for offside in the 20th minute.
Sunderland continued to enjoy the better of proceedings after the interval and were eventually rewarded as Fletcher found the net with 11 minutes remaining.
Wickham duly followed his fellow striker's lead, firing home from the edge of the area to seal victory.