Alexander-Arnold was booed by some Liverpool fans during their clash with Arsenal at Anfield after announcing his departure.
Van Dijk believes Alexander-Arnold might have anticipated the negative reaction but says he must deal with it.
Van Dijk and Mohamed Salah, who were also in the final year of their contracts, chose to renew, unlike Alexander-Arnold.
The 33-year-old acknowledged a busy summer ahead for Liverpool in the transfer market, emphasising the need for additions to retain their Premier League title.