Callum Wilson netted his a goal on his England debut to make it 3-0 in the 77th minute, and after the match Guzan said he and his defenders were determined to stop Rooney as the home side repeatedly force-fed him the ball in risky positions.
Rooney received a warm reception before and after coming on for his 120th appearance for England, who prepared for Sunday's crunch Nations League clash with Croatia by beating the US 3-0 thanks to goals from Jesse Lingard, Trent Alexander-Arnold and Wilson.
England will need to beat Croatia on Sunday to move into the UEFA NL final phase, reports Efe news.
He told Sky Sports, per Goal: "There are times when you doubt yourself as a player, you think: 'Am I good enough?'"
'Great for Callum to get his goal - he probably would feel he might have had that earlier in the game - so some good moments there. "We've had real shoots of progress and achieved some outstanding results", said Southgate. "We haven't had that discussion because of his parade, but we'll be making that point".
Southgate did not want to fix a time in the game when Rooney would come on but said he had discussed it with the 33-year-old. "Everyone in the dressing room has enjoyed it".
If City are proven to have these breached rules, which Chelsea are also under investigation for doing, they could be banned from registering new players for a one-year span.
'He has been brilliant I have to say.
It meant Alexander-Arnold is the youngest Reds player to score for England since Michael Owen registered against Luxembourg in September 1999. We will give him a guard of honor. We will have to be better without the ball, in particular.
"It's shown the quality that Croatia have", Southgate said.
The 33-year-old is now plying his trade over in the States with DC United, where he has settled in brilliantly.