While Koeman’s first-team were coming from two goals down to beat Liverpool 3-2 at St Mary’s, Rodriguez was playing a starring role for Martin Hunter’s side as they beat their Reds counterparts 5-0.
Rodriguez played 80 minutes in the convincing Barclays Under-21 Premier League win as he continued to step up his recovery after a long injury lay-off.
Speaking about the forward’s goals, Koeman said: “It’s fantastic. That’s news what we like to hear.
“First of all the performance of the Under-21s and the three points against Liverpool away is great.
“And of course a hat-trick from Jay is an amazing impact for him and that’s the most important.
“It makes the day even more special.”