Former United favourite Keane tore into Solskjaer's flops following last weekend's shocking 1-0 defeat to Arsenal at Old Trafford that left them in 15th place in the Premier League table.
Keane claimed United lacked players with heart and character - and fears the crop of flops will end up getting Solskjaer the sack.
But Solskjaer reckons he has enough stars with the bottle needed to get United out of the hole they find themselves in.
Solskjaer, whose side travel to Turkey to take on Istanbul Basaksehir in Group H of the Champions League on Wednesday, said: "Roy has always been outspoken, but I'm very glad I have the players we've got here.
"We've got different jobs and Roy's job is to give his opinion. I always listen to Roy, but we always move on here with a great group of players, a strong group of players - and I'm sure we'll see a response."
Despite their domestic failures United have made a stunning return to the Champions League, with impressive wins at PSG and home to RB Leipzig.
Another win in the Turkish capital would see United put one foot in the knockout stages and Solskjaer believes his side could even be good enough to go on and win the competition for the first time since 2008.
He added: "The results can sway the whole picture so many times. These two results have shown the quality we have, but we are not going to get too far ahead of ourselves.
"We look forward to the next game and will keep working to get that consistency. Us at our best level, we can beat anyone and that's how we need to go into every game."