The former Manchester United coach, who had only recently joined the backroom staff at Craven Cottage, believes the struggling side have to invest in new players in January
Jol was relieved of his duties on Sunday, some 24 hours after a 3-0 loss at West Ham made it six defeats in a row in all competitions for Fulham, who are in the bottom three.
Nine defeats from their 13 Premier League games this season have dumped Fulham into the bottom three, with Meulensteen added to Jol's backroom staff last month in a bid to help his fellow Dutchman halt the club's slump in fortunes.
Meulensteen, who has been put in charge of first-team affairs at Craven Cottage, told BBC Radio: "I had some other personal business to attend and suddenly found out that Martin was gone.
"It has been quite a stretch before I decided to join Fulham and the meetings I had with people at the club including Martin Jol were very important to that.
"Eventually it was to work alongside Martin, stay in the Premier League and to make sure we can take Fulham to the next step."
Meulensteen said he has spoken to Jol since news of his departure broke and insists that there are no hard feelings between the pair.
"As soon as I found out I rang him and had a long conversation with him," he added.
"There are no hard feelings between him and myself because I've known Martin for over 25 years and we have a fantastic understanding with each other and I really enjoyed working with him and was looking forward to working with him in the near future to ensure we can turn this corner.
"We were both confident we were capable of doing it but unfortunately events have decided differently."
Moving forward, Meulensteen is confident that Fulham can begin to climb the table and arrest a worrying slide, starting with Tottenham on Wednesday.
However, he believes the players and staff have to improve and some investment might be required in January.
He said: "You have to be realistic. Tables don't lie and you are there for a reason, whether it's a lack of quality or luck, but you are where you are and the most important thing is to make sure that we create a platform to get away from that position as quickly as we can.
"Of course we can [avoid relegation] because it is still before the new year. We've got games to play, we've got January coming up and I think everybody at the club needs to realise that we need to invest.
"And by invest I mean in terms of as a players squad. We need to make sure the players take the responsibility and put everything in place in terms of work rate and discipline and take responsibility to make sure we get better results.
"We as a staff need to do the same and we need to look in to see how we can strengthen this current squad to make sure we can guarantee the best possible situation for Fulham to stay in the Premier League."