The Russia international has not started a Barclays Premier League match since November 10 and, aside from a full game in the FA Cup victory at Scunthorpe, has seen just 28 minutes of top-flight action since.
Pienaar completed his £3million transfer to Tottenham and Bilyaletdinov is now hoping to convince manager David Moyes he is the man to fill the void left by the 28-year-old's departure.
Opportunity: Bilyaletdinov (right) fancies a bigger role at Goodison Park
'Steven has been a big player for Everton for four years and I have to say good luck to him,' he said.
'He's a very creative player and it's not good for Everton that he's gone, but we still have many good players to keep us moving forward.
'Maybe Steven going will be good for me, but I'd prefer to play with him because he's an intelligent player.
'Just because he's gone it doesn't mean I'll start the next game, but who knows?
'Whether I'll get more chances now isn't a question for me, it's a question for David Moyes and Steve Round (assistant manager).'
Time for a change: Midfielder Pienaar (left) has decided to join Tottenham
Pienaar's contract at Goodison Park was due to expire in June and he had made his intentions clear since the end of last season.
Moving is not an option for Bilyaletdinov, who joined the Toffees in the summer of 2009 for around £9m.
'I like this club, I like this team and the atmosphere here is great,' he told the Liverpool Echo.
'I don't think about changing (clubs). The only thing I want to change is the amount of time I spend on the pitch. All I can do is work hard and do my best in training.
'I don't think it's correct to go to the coach and ask him (why I'm not playing). I'm not going to go to the manager crying about it as I've got to be professional.'
Tweet deal for Harry! Pienaar seals move to Spurs after rejecting ChelseaClub-by-club guide to every Premier League transfer deal during JanuaryWatch all the Premier League goals every week on our brilliant video playerAll the latest Everton news, features and opinion
Explore more:People: David Moyes Places: Russia