Scripture also says:
1 Peter 2:21
For even hereunto were ye called: because Christ also suffered for us, leaving us an example, that ye should follow his steps:

Therefore, we are to suffer for the salvation of our brethren as Christ suffered for us.

Scripture says elsewhere:
Colossians 1:24
Who now rejoice in my sufferings for you, and fill up that which is behind of the afflictions of Christ in my flesh for his body's sake, which is thechurch:

And again:
2 Corinthians 1:5For as the sufferings of Christ abound in us, so our consolation also aboundeth by Christ.
6And whether we be afflicted, it is for your consolation and salvation, which is effectual in the enduring of the same sufferings which we also suffer: or whether we be comforted, it is for your consolation and salvation.
7And our hope of you is stedfast, knowing, that as ye are partakers of the sufferings, so shall ye be also of the consolation

Therefore, the Catholic Teaching of the redemptive value of suffering is completely in line with Scripture.  And this is why, the Catholic Church expects us to fast and give up certain things during Lent.  In order that we may imitate Christ and unite ourselves to His suffering.