Their 1-0 win over Liverpool, their first at Anfield in their history, took the Cottagers level with the eighth-placed Reds on 49 points.
One more win would virtually guarantee them a top-10 finish but McKinlay has stressed they should not settle for that.
"We have got a good side and we have always known that," said the coach, who has stood in for ill manager Martin Jol for the last two matches.
"I don't think you need to shout from the rooftops. We think we have a good club there, we do our business in the correct manner and hopefully that transmits on to the football pitch.
"We have had a good three or four years and we want to keep progressing and challenge at the top of the table.
"Standing still means you are moving backwards. It is onwards and upwards, that is the message we try to push at the club."
McKinlay felt the way Fulham bounced back from a woeful 4-0 hammering at Everton three days previously was a credit to the players, nine of whom started at Goodison Park.
"I re-iterated to them why we didn't do so well on Saturday," added McKinlay.
"They are an experienced bunch of players and they know the score.
"I gave them a little reminder of what we are capable of and what we needed to get back to."
Martin Skrtel's fifth-minute own goal proved the difference and it was created by two former Liverpool players, with John Arne Riise crossing for ex-youth team player Alex Kacaniklic to deflect into the path of the Slovakia defender.
"It was good to be back because obviously I spent three years here," Kacaniklic told fulhamfc.com.
"The most important thing was that we won the game of course but it was good to be back playing here with Fulham.
"I'm not sure if I can claim that as an assist because I didn't know too much about it.
"It was lucky it took a touch off the defender because it probably would never have gone in otherwise.
"It is a great achievement because that puts us level on points with Liverpool but we already knew we were a good team because we've got some really great players here so I'm not overly surprised that we won."