The former Ajax ace has been in excellent form for both club and country this season, and is well established as one of the best attacking midfielders in the Premier League.
Hareide claimed Eriksen should be considered among the world's best players, stating that he believes Eriksen is in the top 10 of the world after almost single-handedly disposing of Martin O'Neill's side on Tuesday night.
"It's difficult to rank, but we saw [in Tottenham's Champions League matches] against Real Madrid he is probably one of the best players in his position in Europe at the moment," Hareide said.
"Ronaldo, Messi and some strikers are playing as forwards. Christian is more a wide man or a central midfield player. He has this capability of scoring goals, making assists, finding space, so, definitely top 10."
Eriksen gave Denmark the lead with an excellent curling effort that hit the underside of Darren Randolph's bar and dropped into the net, making the score 2-1 on the night after the first leg ended in a 0-0 draw.
He then added a second with left-footed effort from distance before capitalising on a loose ball to fire into the top corner to take home the match ball, with Nicklas Bendtner and a Cyrus Christie own goal seeing Ireland crash out of the World Cup.
Eriksen has now taken his tally to 10 goals in 20 games for both club and country, and is expected to start in Mauricio Pochettino's Tottenham side on Saturday as Spurs take on bitter rivals Arsenal at the Emirates Stadium.