John Collins, of Fulham, admitted sympathy with Tranmere's plight as they battle to beat the drop, while Fulham are now in touching distance of the Premiership, 17 points clear of second-placed Bolton.
"We got off to a fine start with the early goal, but you've got to give Tranmere credit. They kept going and made it hard for us at times," said the Fulham assistant boss.
"We have set high standards from the very first game of the season and the whole team played well tonight.
"Tranmere put us under pressure at the start of the second half, but fortunately we did not concede.
"You've got to feel sorry for Tranmere, but fingers crossed, they'll get enough points to stay up. We would certainly like to see them stay in Division One.
Fulham midfielder Sean Davis was delighted that a perfect week for him had been ended with a fine victory over Tranmere that emphasises his side's claims for a Premiership place.
Davis made his England Under-21 bow a week ago against Finland and also played against Albania, and returned to play a crucial role in Fulham's 4-1 Prenton Park win.
"It's been a good week for me. I won two caps for the Under-21s and now this rounds it off.
Fulham are now in touching distance of the Premiership, 17 points clear of second-placed Bolton.
"We haven't scored many goals of late and this crowned the performance to get four goals. They were fighting to prove themselves but we worked hard and got the goals we needed.
The secret of Fulham's success is that old favourite - sheer workrate, according to Davis. "We work hard in training and the gaffer shows us what he wants defensively," Davis revealed.
"The club has come on leaps and bounds - with the training ground, diets and such. You can tell why we are top of the league. Jean Tigana's done wonders for me and I enjoy my football at the moment and that is the main thing."
"Tranmere caretaker boss Kevin Sheedy had no complaints after the defeat which leaves Rovers without a win in seven games and entrenched in the relegation battle at the foot of the table.
"It was a harsh lesson, but hopefully not the killer blow," said Sheedy, whose side are five points away from safety.
"We've got to pick ourselves up. We can't feel sorry for ourselves.
"We've got to work hard and go to Grimsby in the hope of getting a result. There are still eight games to go.
"Fulham are head and shoulders above everybody in the division. We were always playing catch-up. We battled and did our best, but they were the better team.
"The supporters were tremendous and I'm only sorry they have gone home very disappointed.
"We allowed Fulham to play their own game in the opening half and they took away a lot of our energy and it showed in the last half hour."
Source sportinglife