Songo'o, who was signed on-loan from Blackburn on Saturday morning, strolled through the Scottish Premiership match and is looking to follow in his goalkeeping father's footsteps by playing for Cameroon in Brazil this summer.
"My father Jacques is such an inspirational figure for me," the 22-year-old said. "He is a legend in Cameroon. He played in the World Cup, in the Champions League and also won La Liga with Deportivo La Coruna.
"He had an unbelievable career and is now the goalkeeping coach with the national team.
"I would like to do the same and my aim is now to try and play in the World Cup this summer.
"I have played in the Under-20 World Cup and that was an incredible feeling. To do it for the first team would be unbelievable."
All six of Derek Adams' January signings started the game as County made it 10 points from a possible 12 in 2014.
On-loan Cardiff midfielder Filip Kiss took his tally to four goals in two matches, opening the scoring three minutes before the break when he headed home Graham Carey's cross, and rounding it off in the 74th minute with a spectacular 30-yard strike.
Debutant Yoann Arquin was on target five minutes earlier when he chested home a shot from another Blackburn loan player, Jordan Slew.
Songo'o said: "I was surprised how impressive Ross County were. It was an unbelievable performance.
"If we keep playing like this then we will keep going up the league table."
Dundee United defender Keith Watson admitted their six-match run without a win was taking its toll.
"We started the game quite brightly but didn't take a couple of wee sniffs," he said. "After they scored our heads went down and it just wasn't good enough from us.
"After a great run that's six without a win and I think it's starting to get to a few of the boys and the way we played it showed a little. We were getting frustrated when it was still 1-0 and didn't play like we know we can."
Manager Jackie McNamara will hope his decision to send teenagers Ryan Gauld and John Souttar on holiday to Spain is vindicated by getting them back rejuvenated for the upcoming derby against St Johnstone.
Watson added: "It's as if we've lost a bit of confidence and we need to get it back quick. We need to put this game behind us and not think about it again because it was so poor from us.
"With the group of players we've got and the squad we have we should be winning and getting results anywhere."