Everton broke the British transfer record back in 1988 when they signed Cottee from West Ham - the club he had supported all his life - for £2.2million.
Although the fee was eclipsed by Liverpool when they paid £2.7million for Ian Rush just a month later, there was still a lot of pressure on the East End export and it soon began to show.
Cottee, who scored 93 goals in 212 appearances during his initial spell with the Irons, scored 13 times in his first two seasons at Goodison Park - a good return, but still nearly half of what the likes of Adam Smith and Gary Lineker were accumulating every year.
Eighteen goals followed over the next two seasons and at the turn of the next campaign, having found the net seven times by February, his confidence had hit rock bottom.
Cottee thought nothing could improve his situation until he heard a thick Essex accent bellow his name from across a deserted Goodison Park a couple of hours after Everton's loss to Tottenham.
"I'd had a drink in the players' lounge and was walking to the car park with my mum and dad when I heard someone shout 'Tony!', Cottee explained.
"It came from the Press box. I couldn't see who it was, but as soon as the guy took his headphones off and walked over to me, I realised it was Bobby Moore. He'd been commentating on the game.
"I was nervous. I was thinking: 'Oh my god, it's Bobby Moore. What's he called me over for?' I had never spoken to him before.
"He shook my hand and just said to me: 'Tony, I just wanted to check that you are okay?'
"He told me he knew it had been a tough time for me at Everton and how difficult it must have been for a London lad to go and live up north, but he told me everything would work out okay and that my form would turn around.
"He told me to believe in myself and that the goals would come again, and they did."
Cottee scored five more times before the season was out and he was soon back on the familiar turf of the Boleyn Ground, where he scored 13 goals to help Harry Redknapp's Irons escape relegation.
Cottee must have recalled the Goodison Park story to every supporter who asks him about Moore - the man who Irons fans continue to idolise two decades on from his death.
"I will always feel grateful for what he did for me that day. It will stay with me forever," Cottee said.
"It gave me a massive lift. I floated across the pitch to get to my car that night. I couldn't believe it. He was a classy man off the pitch as well as on it."
Although Cottee only encountered Moore on one more occasion following that cold February night, the meeting made a lasting impression on the striker, who was asked to represent Everton in a charity match to raise funds for the defender's charity a year after his death from cancer.
Sunday may mark 20 years since Moore's death, but Cottee is determined for the West Ham icon's name to live on for some time yet.
"I've brainwashed my twin boys into becoming fans of the club and if you ask them to name the most famous West Ham player ever they would say Bobby Moore, I guarantee it," he said.







